| Institute for Mathematics and its Applications University of Minnesota 114 Lind Hall 207 Church Street SE Minneapolis, MN 55455 |
Web: http://www.ima.umn.edu |
Email: ima-staff@ima.umn.edu |
Telephone: (612) 624-6066 |
Fax: (612) 626-7370
Additional newsletters available at http://www.ima.umn.edu/newsletters
Additional newsletters available at http://www.ima.umn.edu/newsletters
IMA Newsletter #394
July 2009
2009-2010 IMA Participating Institutions Conferences
IMA Events
PI Summer Graduate Program
The Mathematics of Inverse Problems
June 15 - July 3, 2009
Organizers: Fioralba Cakoni (University of Delaware), David L. Colton (University of Delaware), Russell Luke (University of Delaware), Peter Monk (University of Delaware), R Rakesh (University of Delaware)IMA Workshop
IMA Interdisciplinary Research Experience for Undergraduates
June 29 - July 31, 2009
Organizers: Daniel Flath (Macalester College)Nonlinear Conservation Laws and Applications
July 13-31, 2009
Organizers: Alberto Bressan (Pennsylvania State University), Gui-Qiang G. Chen (Northwestern University), Marta Lewicka (University of Minnesota Twin Cities), Dehua Wang (University of Pittsburgh)
Schedule
Wednesday, July 1
| All Day | Work on projects till afternoon. Lind Hall 400 2:00pm Separate group meetings. Lind Hall 400 | SW6.29-7.31.09 | ||
| 10:45am-11:15am | Coffee break | Lind Hall 400 | ||
| 3:00pm-4:00pm | Organic semiconductors for flexible solar cells | Russell J. Holmes (University of Minnesota) | Lind Hall 409 | SW6.29-7.31.09 |
Thursday, July 2
| All Day | Work on projects till afternoon. Lind Hall 400 | SW6.29-7.31.09 | ||
| 10:45am-11:15am | Coffee break | Lind Hall 400 | ||
| 3:00pm-6:00pm | Mississippi history walk (lecturer: Pat Nunnally) | Mississippi River | SW6.29-7.31.09 |
Friday, July 3
| All Day | Independence Day. The IMA summer REU schedule will take place. | |||
| All Day | 3:00pm All groups meet together. Each group gives presentation on progress and results. Lind Hall 409 | SW6.29-7.31.09 |
Saturday, July 4
| All Day | No events scheduled. | SW6.29-7.31.09 |
Sunday, July 5
| All Day | No events scheduled. | SW6.29-7.31.09 |
Monday, July 6
| All Day | 9:00am Separate group meetings. Work all day on projects. Lind Hall 400 | SW6.29-7.31.09 | ||
| 10:45am-11:15am | Coffee break | Lind Hall 400 |
Tuesday, July 7
| All Day | Work all day on projects. Lind Hall 400 | SW6.29-7.31.09 | ||
| 10:45am-11:15am | Coffee break | Lind Hall 400 |
Wednesday, July 8
| All Day | Work on projects till afternoon. Lind Hall 400 2:00pm Separate group meetings. Lind Hall 400 | SW6.29-7.31.09 | ||
| 10:45am-11:15am | Coffee break | Lind Hall 400 | ||
| 3:00pm-4:00pm | Toward a second order description of neuronal networks | Duane Nykamp (University of Minnesota) | Lind Hall 409 | SW6.29-7.31.09 |
Thursday, July 9
| All Day | Work on projects till afternoon. Lind Hall 400 | SW6.29-7.31.09 | ||
| 10:45am-11:15am | Coffee break | Lind Hall 400 | ||
| 3:00pm-6:00pm | Trip to the Minneapolis Institute of Arts | Minneapolis Institute of Arts 2400 3rd Ave S Minneapolis, MN 55404 (612) 870-3131 |
SW6.29-7.31.09 |
Friday, July 10
| All Day | 3:00pm All groups meet together. Each group gives presentation on progress and results. Lind Hall 409 | SW6.29-7.31.09 | ||
| 10:45am-11:15am | Coffee break | Lind Hall 400 |
Saturday, July 11
| All Day | No events scheduled. | SW6.29-7.31.09 |
Sunday, July 12
| All Day | No events scheduled. | SW6.29-7.31.09 |
Monday, July 13
| All Day |
Morning Chair: Marta Lewicka (University of Minnesota) Afternoon Chair: Alberto Bressan (Penn State University) | SP7.13-31.09 | ||
| All Day | 9:00am Separate group meetings. Work all day on projects. Lind Hall 400 | SW6.29-7.31.09 | ||
| 8:15am-8:45am | Registration and coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 8:45am-9:00am | Welcome to the IMA | Fadil Santosa (University of Minnesota) | EE/CS 3-180 | SP7.13-31.09 |
| 9:00am-10:15am | Introduction to conservation laws | Constantine Dafermos (Brown University) | EE/CS 3-180 | SP7.13-31.09 |
| 10:15am-10:45am | Coffee Break | EE/CS 3-176 | SP7.13-31.09 | |
| 10:45am-11:45am | An introduction to multidimensional conservation laws. Lecture 1 | Gui-Qiang G. Chen (Northwestern University) | EE/CS 3-180 | SP7.13-31.09 |
| 11:45am-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-3:00pm | Asymptotic analysis in thermodynamics of viscous fluids. Lecture 1 | Eduard Feireisl (Czech Academy of Sciences (AVČR)) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-3:30pm | Coffee Break | EE/CS 3-176 | SP7.13-31.09 | |
| 3:30pm-4:45pm | A tutorial on hyperbolic conservation laws. Lecture 1 | Alberto Bressan (Pennsylvania State University) | EE/CS 3-180 | SP7.13-31.09 |
Tuesday, July 14
| All Day | Morning Chair: Gui-Qiang G. Chen
(Northwestern University) Afternoon Chair: Dehua Wang (University of Pittsburgh) | SP7.13-31.09 | ||
| All Day | Work all day on projects. Lind Hall 400 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-10:15am | A tutorial on hyperbolic conservation laws. Lecture 2 | Alberto Bressan (Pennsylvania State University) | EE/CS 3-180 | SP7.13-31.09 |
| 10:15am-10:45am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 10:45am-12:00pm | Asymptotic analysis in thermodynamics of viscous fluids. Lecture 2 | Eduard Feireisl (Czech Academy of Sciences (AVČR)) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-3:00pm | Dynamics of viscous shock waves. Lecture 1: Stability of viscous shock waves | Kevin Zumbrun (Indiana University) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-5:00pm | Selected topics in approximate solutions of nonlinear conservation laws | Eitan Tadmor (University of Maryland) | EE/CS 3-180 | SP7.13-31.09 |
Wednesday, July 15
| All Day | Morning Chair: Eitan Tadmor (University of Maryland) Afternoon Chair: Kevin Zumbrun (Indiana University) | SP7.13-31.09 | ||
| All Day | Work on projects till afternoon. Lind Hall 400 2:00pm Separate group meetings. Lind Hall 400 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-10:15am | Numerical methods for multi-dimensional systems of conservation laws. Lecture 1 | Chi-Wang Shu (Brown University) | EE/CS 3-180 | SP7.13-31.09 |
| 10:15am-10:45am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 10:45am-12:00pm | An introduction to multidimensional conservation laws. Lecture 2 | Gui-Qiang G. Chen (Northwestern University) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-3:00pm | Asymptotic analysis in thermodynamics of viscous fluids. Lecture 3 | Eduard Feireisl (Czech Academy of Sciences (AVČR)) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 3:00pm-4:00pm | Sparse signal representations and applications | Ahmed H. Tewfik (University of Minnesota) | Lind Hall 409 | SW6.29-7.31.09 |
| 4:00pm-5:00pm | Numerical methods for multi-dimensional systems of conservation laws. Lecture 2 | Chi-Wang Shu (Brown University) | EE/CS 3-180 | SP7.13-31.09 |
| 6:30pm-8:30pm | Social dinner for organizers and main speakers | W.A. Frost and Company | SP7.13-31.09 |
Thursday, July 16
| All Day | Morning Chair: Constantine Dafermos
(Brown University) Afternoon Chair: Eduard Feireisl (Czech Academy of Sciences (AVČR)) | SP7.13-31.09 | ||
| All Day | Work on projects till afternoon. Lind Hall 400 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-10:15am | Asymptotic analysis in thermodynamics of viscous fluids. Lecture 4 | Eduard Feireisl (Czech Academy of Sciences (AVČR)) | EE/CS 3-180 | SP7.13-31.09 |
| 10:15am-10:45am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 10:45am-12:00pm | Numerical methods for multi-dimensional systems of conservation laws. Lecture 3 | Chi-Wang Shu (Brown University) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-3:00pm | A tutorial on hyperbolic conservation laws. Lecture 3 | Alberto Bressan (Pennsylvania State University) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 3:00pm-6:00pm | Canoeing trip on Lake Calhoun (in case of rain Mill City Museum) | Lake Calhoun or Mill City Museum | SW6.29-7.31.09 | |
| 4:00pm-5:00pm | Dynamics of viscous shock waves. Lecture 2: Verification of the Evans condition | Kevin Zumbrun (Indiana University) | EE/CS 3-180 | SP7.13-31.09 |
Friday, July 17
| All Day | Morning Chair: Gui-Qiang Chen
(Northwestern University) Afternoon Chair: Alberto Bressan (Penn State University) | SP7.13-31.09 | ||
| All Day | 3:00pm All groups meet together. Each group gives presentation on progress and results. Lind Hall 409 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-10:15am | A tutorial on hyperbolic conservation laws. Lecture 4 | Alberto Bressan (Pennsylvania State University) | EE/CS 3-180 | SP7.13-31.09 |
| 10:15am-10:45am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 10:45am-12:00pm | Dynamics of viscous shock waves.
Lecture 3: Conditional stability and bifurcation | Kevin Zumbrun (Indiana University) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-3:00pm | An introduction to multidimensional conservation laws. Lecture 3 | Gui-Qiang G. Chen (Northwestern University) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-5:00pm | Numerical methods for multi-dimensional systems of conservation laws. Lecture 4 | Chi-Wang Shu (Brown University) | EE/CS 3-180 | SP7.13-31.09 |
Saturday, July 18
| All Day | Chair: Marta Lewicka (University of Minnesota) | SP7.13-31.09 | ||
| All Day | No events scheduled. | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-10:15am | An introduction to multidimensional conservation laws. Lecture 4 | Gui-Qiang G. Chen (Northwestern University) | EE/CS 3-180 | SP7.13-31.09 |
| 10:15am-10:45am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 10:45am-12:00pm | Dynamics of viscous shock waves.
Lecture 4: Multi-dimensional dynamics: flow in an infinite cylinder | Kevin Zumbrun (Indiana University) | EE/CS 3-180 | SP7.13-31.09 |
Sunday, July 19
| All Day | No scheduled activity | SP7.13-31.09 | ||
| All Day | No events scheduled. | SW6.29-7.31.09 |
Monday, July 20
| All Day | Morning Chair: Gui-Qiang G. Chen
(Northwestern University)
Afternoon Chair: Tai-Ping Liu (Stanford University) | SP7.13-31.09 | ||
| All Day | 9:00am Separate group meetings. Work all day on projects. Lind Hall 400 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | Kinetic theory and gas dynamics | Tai-Ping Liu (Stanford University) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| On the classical solutions of two dimensional inviscid rotating shallow water system | Bin Cheng (University of Michigan) | |||
| Gasdynamic regularity and nondegeneracy: some classifying remarks | Liviu Florin Dinu (Romanian Academy of Sciences) | |||
| On the approximation of conservation laws by vanishing viscosity | Carlotta Donadello (Northwestern University) | |||
| Non-uniqueness of entropy solutions and the carbuncle phenomenon | Volker Wilhelm Elling (University of Michigan) | |||
| Optimal nodal control of networked systems of conservation laws | Michael Herty (RWTH Aachen) | |||
| Global strong solutions to density-dependent viscoelasticity and liquid crystal | Xianpeng Hu (University of Pittsburgh) Dehua Wang (University of Pittsburgh) | |||
| Modulational instability of periodic waves | Mathew A. Johnson (Indiana University) | |||
| Compressible turbulence modelling in astrophysics | Christian F Klingenberg (Bayerische-Julius-Maximilians-Universität Würzburg) | |||
| L2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method | Nicholas Matthew Leger (University of Texas) | |||
| On the motion of several rigid bodies in an incompressible non-Newtonian and heat-conducting fluid | Sarka Necasova (Czech Academy of Sciences (AVČR)) | |||
| Stability of noncharacteristic viscous boundary layers | Toan Nguyen (Indiana University) | |||
| Elasticity of thin shells and Sobolev spaces of isometries | Reza Pakzad (University of Pittsburgh) | |||
| A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws | Arshad Ahmud Iqbal Peer (University of Mauritius) | |||
| On an inhomogeneous slip-inflow boundary value problem for a steady flow of a viscous compressible fluid in a cylindrical domain | Tomasz Piotr Piasecki (Polish Academy of Sciences) | |||
| The Riemann problem for the stochastically perturbed non-viscous Burgers equation and the pressureless gas dynamics model | Olga Rozanova (Moscow State University) | |||
| Elastodynamics, differential forms, and weak solutions | David H. Wagner (University of Houston) | |||
| Central schemes for a new class of entropy solutions of the modified Buckley-Leverett equation | Ying Wang (Ohio State University) | |||
| Strong waves and vaccums in isentropic gas dynamics | Robin Young (University of Massachusetts) | |||
| Periodic solutions to the Euler equations | Robin Young (University of Massachusetts) | |||
| 11:00am-11:50am | Existence and stability of global solutions to shock reflection problem | Mikhail Feldman (University of Wisconsin) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-2:50pm | Stability of multidimensional contact discontinuities in compressible MHD | Ya-Guang Wang (Shanghai Jiaotong University) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-4:50pm | Discussion: Kinetic theory and gas dynamics | Tai-Ping Liu (Stanford University) | EE/CS 3-180 | SP7.13-31.09 |
Tuesday, July 21
| All Day | Work all day on projects. Lind Hall 400 | SW6.29-7.31.09 | ||
| All Day | Morning Chair: Mikhail Feldman
(University of Wisconsin) Afternoon Chair: Benoit Perthame (Université de Paris VI (Pierre et Marie Curie)) | SP7.13-31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | A coupled system of elliptic/conservation law arising in cell self-organization | Benoit Perthame (Université de Paris VI (Pierre et Marie Curie)) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 11:00am-11:50am | Transonic flows and isometric embeddings | Dehua Wang (University of Pittsburgh) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-2:50pm | Instantaneous boundary-tangency of singularity curves in compressible fluid flow | David Hoff (Indiana University) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-4:50pm | Discussion: Coupling Hyperbolic and elliptic/parabolic systems: state of the art, open problems, new models | Benoit Perthame (Université de Paris VI (Pierre et Marie Curie)) | EE/CS 3-180 | SP7.13-31.09 |
Wednesday, July 22
| All Day | Morning Chair: Marta Lewicka
(University of Minnesota) Afternoon Chair: Denis Serre (École Normale Supérieure de Lyon) | SP7.13-31.09 | ||
| All Day | Work on projects till afternoon. Lind Hall 400 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | The nature of viscous dissipation in systems of conservation laws | Denis Serre (École Normale Supérieure de Lyon) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 11:00am-11:50am | Kinetic relations and beyond | Lev Truskinovsky (École Polytechnique) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-2:50pm | Quantum fluids and related problems | Pierangelo Marcati (Università di L'Aquila) | EE/CS 3-180 | SP7.13-31.09 |
| 2:00pm-3:00pm | The development of a similarity solution for a Stefan like problem, with two moving boundaries, related to the growth of a sediment ocean basin | Vaughan R. Voller (University of Minnesota) | Lind Hall 409 | SW6.29-7.31.09 |
| 3:00pm-3:10pm | Group Photo | SP7.13-31.09 | ||
| 3:10pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-4:50pm | Discussion: Dissipation in systems of conservation laws | Denis Serre (École Normale Supérieure de Lyon) | EE/CS 3-180 | SP7.13-31.09 |
Thursday, July 23
| All Day | Work on projects till afternoon. Lind Hall 400 | SW6.29-7.31.09 | ||
| All Day | Morning Chair: Pierangelo Marcati
(Università di L'Aquila) Afternoon Chair: Nader Masmoudi (New York University) | SP7.13-31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | Global existence for small data water waves | Nader Masmoudi (New York University) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 11:00am-11:50am | Kinetic relations for undercompressive shocks. Physical, mathematical, and numerical issues | Philippe G. LeFloch (Université de Paris VI (Pierre et Marie Curie)) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 1:30pm-5:00pm | Trip to the State Capitol/Downtown St. Paul | State Capitol/Downtown St. Paul | SW6.29-7.31.09 | |
| 2:00pm-2:50pm | Reduced theories in nonlinear elasticity | Marta Lewicka (University of Minnesota) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-4:50pm | Discussion: Free boundary problems related to water waves | Nader Masmoudi (New York University) | EE/CS 3-180 | SP7.13-31.09 |
| 6:30pm-8:30pm | Workshop dinner at Kikugawa at Riverplace | Kikugawa at Riverplace 43 Main Street SE Minneapolis MN 55414 612-378-3006 |
SP7.13-31.09 |
Friday, July 24
| All Day | Morning Chair: Helge Holden
(Norwegian University of Science and Technology (NTNU)) Afternoon Chair: Luigi Ambrosio (Scuola Normale Superiore) | SP7.13-31.09 | ||
| All Day | 3:00pm All groups meet together. Each group gives presentation on progress and results. Lind Hall 409 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | Flows in the space of probability measures and convergence of Wigner transforms | Luigi Ambrosio (Scuola Normale Superiore) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 11:00am-11:50am | Monge problem in geodesic spaces | Stefano Bianchini (International School for Advanced Studies (SISSA/ISAS)) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-2:50pm | Optimal transport for the system of isentropic Euler equations | Michael Westdickenberg (Georgia Institute of Technology) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-4:50pm | Discussion: Continuity equations and flows: recent results and open problems | Luigi Ambrosio (Scuola Normale Superiore) | EE/CS 3-180 | SP7.13-31.09 |
Saturday, July 25
| All Day | Chair: Athanasios Tzavaras (University of Maryland) | SP7.13-31.09 | ||
| All Day | No events scheduled. | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | Convergence of operator splitting for the KdV equation | Helge Holden (Norwegian University of Science and Technology (NTNU)) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 11:00am-11:50am | Well-posedness results for the transport equation, and applications to the chromatography system | Laura Valentina Spinolo (Scuola Normale Superiore) | EE/CS 3-180 | SP7.13-31.09 |
Sunday, July 26
| All Day | No scheduled activity. | SP7.13-31.09 | ||
| All Day | No events scheduled. | SW6.29-7.31.09 |
Monday, July 27
| All Day | Morning Chair: Alberto Bressan
(Penn State University) Afternoon Chair: Yuxi Zheng (Pennsylvania State University) | SP7.13-31.09 | ||
| All Day | 9:00am Separate group meetings. Work all day on projects. Lind Hall 400 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | Semi-hyperbolic patches of solutions to two-dimensional compressible Euler systems | Yuxi Zheng (Pennsylvania State University) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| Rarefaction wave interaction for the unsteady transonic small disturbance equation | Katarina Jegdic (University of Houston-Downtown) | |||
| 11:00am-11:50am | Nonlinear surface waves and the loss of uniform Lopatinski stability in IBVPs for hyperbolic conservation laws | John K. Hunter (University of California, Davis) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-2:50pm | Symmetric waves for conservation laws | Helge Kristian Jenssen (Pennsylvania State University) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-4:50pm | Discussion | Yuxi Zheng (Pennsylvania State University) | EE/CS 3-180 | SP7.13-31.09 |
Tuesday, July 28
| All Day | Morning Chair: Barbara Keyfitz
(Ohio State University) Afternoon Chair: Athanasios Tzavaras (University of Maryland) | SP7.13-31.09 | ||
| All Day | Work all day on projects. Lind Hall 400 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | Adiabatic shear bands in high strain-rate plasticity | Athanasios E. Tzavaras (University of Maryland) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| Global BV for a model of granular flow | Wen Shen (Pennsylvania State University) | |||
| The slow erosion limit in a model of granular flow | Wen Shen (Pennsylvania State University) | |||
| 11:00am-11:50am | Global BV for a model of granular flow | Wen Shen (Pennsylvania State University) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-2:50pm | Homogenization of degenerate porous medium type equations in ergodic algebras | Hermano Frid (Institute of Pure and Applied Mathematics (IMPA)) | EE/CS 3-180 | SP7.13-31.09 |
| 2:50pm-6:00pm | Trip to St. Anthony Falls Laboratory | St. Anthony Falls Laboratory | SW6.29-7.31.09 | |
| 3:00pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-4:50pm | Discussion: Conservation laws in elasticity | Athanasios E. Tzavaras (University of Maryland) | EE/CS 3-180 | SP7.13-31.09 |
Wednesday, July 29
| All Day | Work on projects till afternoon. Lind Hall 400 2:00pm Separate group meetings. Lind Hall 400 | SW6.29-7.31.09 | ||
| All Day | Morning Chair: Dehua Wang (University of Pittsburgh)
Afternoon Chair: James G. Glimm (SUNY) | SP7.13-31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | Mathematical and numerical principles for turbulent mixing | James G. Glimm (SUNY) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 11:00am-11:50am | Charge transport in an incompressible fluid medium | Joseph W. Jerome (Northwestern University) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-2:50pm | Stability of rotating white dwarf stars | Tao Luo (Georgetown University) | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 3:00pm-4:00pm | Modeling the earth's glacial cycles | Richard P. McGehee (University of Minnesota) | Lind Hall 409 | SW6.29-7.31.09 |
| 4:00pm-4:50pm | Discussion topic: Conservation laws in higher spatial dimensions: Euler vs. Navier-Stokes; theory and computation | James G. Glimm (SUNY) | EE/CS 3-180 | SP7.13-31.09 |
Thursday, July 30
| All Day | Morning Chair: Joseph W. Jerome
(Northwestern University) Afternoon Chair: Suncica Canic (University of Houston) | SP7.13-31.09 | ||
| All Day | Work on projects. Lind Hall 400 Evaluations solicited. Lind Hall 400 4:30 pm Final written report (LaTeX) and high quality poster due. Lind Hall 409 | SW6.29-7.31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | A hyperbolic-parabolic 3D axially symmetric fluid-structure interaction problem arising in blood flow modeling | Suncica Canic (University of Houston) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 11:00am-11:50am | Global regularity of solutions to systems of reaction-diffusion with sub-quadratic growth in any dimension | Alexis Frederic Vasseur (University of Texas) | EE/CS 3-180 | SP7.13-31.09 |
| 12:00pm-2:00pm | Lunch | SP7.13-31.09 | ||
| 2:00pm-2:50pm | Conservation laws on networks | Mauro Garavello (Università del Piemonte Orientale "Amedeo Avogadro") | EE/CS 3-180 | SP7.13-31.09 |
| 3:00pm-4:00pm |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 4:00pm-4:50pm | Discussion | Suncica Canic (University of Houston) | EE/CS 3-180 | SP7.13-31.09 |
| 6:30pm-8:30pm | Workshop dinner at Pagoda | Pagoda Restaurant 1417 4th St. SE Minneapolis, MN 612-378-4710 |
SP7.13-31.09 |
Friday, July 31
| All Day | 10:00am-11:00am Poster Session,
Lind Hall 400
11:00am-11:30am Closing, Lind Hall 409 | SW6.29-7.31.09 | ||
| All Day | Chair: Alberto Bressan (Penn State University) | SP7.13-31.09 | ||
| 8:30am-9:00am | Coffee | EE/CS 3-176 | SP7.13-31.09 | |
| 9:00am-9:50am | Well posedness and control in models based on conservation laws | Rinaldo Mario Colombo (Università di Brescia) | EE/CS 3-180 | SP7.13-31.09 |
| 10:00am-11:00am |
Coffee Break and Poster Session Poster submissions welcome from all participants Instructions | EE/CS 3-176 | SP7.13-31.09 | |
| 11:00am-11:50am | The sonic line as a free boundary: Stability under perturbations | Barbara Lee Keyfitz (Ohio State University) | EE/CS 3-180 | SP7.13-31.09 |
| 11:50am-12:00pm | Closing Remarks | EE/CS 3-180 | SP7.13-31.09 |
Event Legend: |
|
| SP7.13-31.09 | Nonlinear Conservation Laws and Applications |
| SW6.29-7.31.09 | IMA Interdisciplinary Research Experience for Undergraduates |
Abstracts
| Luigi Ambrosio (Scuola Normale Superiore) | Flows in the space of probability measures and convergence of Wigner transforms |
| Abstract: We provide an extension of the theory of flows in Euclidean spaces associated to wekly differentiable velocity fields, replacing the Euclidean state space with the space of probability measure. This way, the continuity equation can be viewed as an ODE in the space of probability measures and we provide some well-posedness and stability results. We illustrate, as an example and a basic motivation for the development of the theory, the problem of convergence of Wigner transforms in Quantum Mechanics. | |
| Luigi Ambrosio (Scuola Normale Superiore) | Discussion: Continuity equations and flows: recent results and open problems |
| Abstract: No Abstract | |
| Stefano Bianchini (International School for Advanced Studies (SISSA/ISAS)) | Monge problem in geodesic spaces |
| Abstract: No Abstract | |
| Alberto Bressan (Pennsylvania State University) | A tutorial on hyperbolic conservation laws. Lecture 1 |
Abstract: This set of lectures will provide a basic introduction to
hyperbolic systems of conservation laws in one space dimension.
The main topics covered will be:
|
|
| Alberto Bressan (Pennsylvania State University) | A tutorial on hyperbolic conservation laws. Lecture 2 |
| Abstract: Same abstract as lecture 1. | |
| Alberto Bressan (Pennsylvania State University) | A tutorial on hyperbolic conservation laws. Lecture 3 |
| Abstract: Same abstract as lecture 1. | |
| Alberto Bressan (Pennsylvania State University) | A tutorial on hyperbolic conservation laws. Lecture 4 |
| Abstract: Same abstract as lecture 1. | |
| Suncica Canic (University of Houston) | A hyperbolic-parabolic 3D axially symmetric fluid-structure interaction problem arising in blood flow modeling |
| Abstract: No Abstract | |
| Suncica Canic (University of Houston) | Discussion |
| Abstract: No Abstract | |
| Gui-Qiang G. Chen (Northwestern University) | An introduction to multidimensional conservation laws. Lecture 1 |
Abstract: This series of four lectures will provide an introduction
to multidimensional conservation laws, along with a perspective on a
list of open problems. The main topics will include:
Lecture References:
*You may directly download them from http://www.math.northwestern.edu/~gqchen/preprints/ |
|
| Gui-Qiang G. Chen (Northwestern University) | An introduction to multidimensional conservation laws. Lecture 2 |
| Abstract: Same abstract as lecture 1. | |
| Gui-Qiang G. Chen (Northwestern University) | An introduction to multidimensional conservation laws. Lecture 3 |
| Abstract: Same abstract as lecture 1. | |
| Gui-Qiang G. Chen (Northwestern University) | An introduction to multidimensional conservation laws. Lecture 4 |
| Abstract: Same abstract as lecture 1. | |
| Bin Cheng (University of Michigan) | On the classical solutions of two dimensional inviscid rotating shallow water system |
| Abstract: Joint work with with Chunjing Xie. We prove global existence and asymptotic behavior of classical solutions for two dimensional inviscid Rotating Shallow Water system with small initial data subject to the zero-relative-vorticity constraint. Such global existence is in contrast with the finite time breakdown of compressible Euler equations in two and three dimensions. A key step in our proof is reformulation of the problem into a symmetric quasilinear Klein-Gordon system, which is then studied with combination of the vector field approach and the normal forms. We also probe the case of general initial data and reveal a lower bound for the lifespan that is almost inversely proportional to the size of the initial relative vorticity. | |
| Rinaldo Mario Colombo (Università di Brescia) | Well posedness and control in models based on conservation laws |
| Abstract: Given a model based on a conservation law, we study how the solution depends from the initial/boundary datum, from the flow and from various constraints. With this tool, several control problems can be addressed and the existence of an optimal control can be proved. Models describing escape dynamics of pedestrians, traffic at toll gates, open canals management and fluid flow in gas pipelines fall within this framework. In particular, a necessary condition for optimality is obtained, which applies to a supply chain model. | |
| Constantine Dafermos (Brown University) | Introduction to conservation laws |
| Abstract: I am planning to convey a feel for the area by touching upon its history, its general features, the current directions, etc., paving the way for the more technical lectures by others. | |
| Liviu Florin Dinu (Romanian Academy of Sciences) | Gasdynamic regularity and nondegeneracy: some classifying remarks |
| Abstract: We consider two gasdynamic contexts: an isentropic context and, respectively, an anisentropic context of a special type. Some [multidimensional] classes of regular solutions [simple waves solutions and regular interactions of simple waves solutions] can be constructively associated to the isentropic context, in presence of an ad hoc requirement of genuine nonlinearity, via a Burnat type ["algebraic"] approach [centered on a duality connection between the hodograph character and the physical character]. The "algebraic" construction fails generally [for geometrical and/or physical reasons] in the mentioned anisentropic context. Incidentally, in this case the "algebraic" construction can be replaced by a Martin type ["differential"] approach [centered on a Monge-Ampere type representation]. Some classes [unsteady 1D; steady supersonic] of regular solutions [pseudo simple waves solutions, regular interactions of pseudo simple waves solutions] can be constructed in this case via a "linearized" version of the "differential" approach. Some contrasts and consonances are considered, in a classifying parallel, between the two approaches ["algebraic", "differential"] and the two classes [isentropic, anisentropic] of regular solutions respectively associated. This is a joint work with Marina Ileana Dinu. | |
| Carlotta Donadello (Northwestern University) | On the approximation of conservation laws by vanishing viscosity |
| Abstract: We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. After the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient. | |
| Volker Wilhelm Elling (University of Michigan) | Non-uniqueness of entropy solutions and the carbuncle phenomenon |
| Abstract: In one space dimension, the Godunov scheme can only converge to entropy solutions, for which uniqueness theorems in various classes are known. We present an example in 2d where the Godunov scheme converges, depending on the grid, either to an exact entropy solution or to a second, numerical solution, which is also produced by all other numerical schemes tested. We propose that entropy solutions are not unique in 2d. The observation also yields an explanation for the "carbuncle phenomenon", an instability in numerical calculations of shock waves. Thus fundamental consequences both for numerics and theory. | |
| Eduard Feireisl (Czech Academy of Sciences (AVČR)) | Asymptotic analysis in thermodynamics of viscous fluids. Lecture 1 |
Abstract: Singular limits in the theory of partial differential equations
represent a class of problems, where some parameters in the equations become
small or infinitely large. We discuss the singular limits arising in the scale
analysis of energetically isolated fluid systems. In particular,
the following topics are addressed:
|
|
| Eduard Feireisl (Czech Academy of Sciences (AVČR)) | Asymptotic analysis in thermodynamics of viscous fluids. Lecture 2 |
| Abstract: Same abstract as lecture 1. | |
| Eduard Feireisl (Czech Academy of Sciences (AVČR)) | Asymptotic analysis in thermodynamics of viscous fluids. Lecture 3 |
| Abstract: Same abstract as lecture 1. | |
| Eduard Feireisl (Czech Academy of Sciences (AVČR)) | Asymptotic analysis in thermodynamics of viscous fluids. Lecture 4 |
| Abstract: Same abstract as lecture 1. | |
| Mikhail Feldman (University of Wisconsin) | Existence and stability of global solutions to shock reflection problem |
| Abstract: In this talk we will start with discussion of shock reflection phenomena. Then we describe recent results on existence and stability of global solutions to regular shock reflection for potential flow for all wedge angles up to the sonic angle, and discuss the techniques. The approach is to reduce the shock reflection problem to a free boundary problem for a nonlinear elliptic equation, with ellipticity degenerate near a part of the boundary (the sonic arc). We will discuss techniques to handle such free boundary problems and degenerate elliptic equations. This is a joint work with Gui-Qiang Chen. | |
| Hermano Frid (Institute of Pure and Applied Mathematics (IMPA)) | Homogenization of degenerate porous medium type equations in ergodic algebras |
| Abstract: No Abstract | |
| Mauro Garavello (Università del Piemonte Orientale "Amedeo Avogadro") | Conservation laws on networks |
| Abstract: In this talk we consider a conservation law (or a system of conservation laws) on a network consisting in a finite number of arcs and vertices. This setting is justified by various applications, such as car traffic, gas pipelines, data networks, supply chains, blood circulation and so on. The key point in the extension of conservation laws on networks is to define solutions at vertices. Indeed, it is sufficient to define solutions only for Riemann problems at vertices, i.e. Cauchy problems with constant initial data in each arc of the junction. We present some different possibilities to produce solutions to Riemann problems at vertices. Moreover we consider the general Cauchy problem on the network. We explain how to prove existence of a solution both in the scalar case and in the case of systems. In particular, for the scalar case, we introduce general properties on Riemann solvers at vertices, which permit to have existence of solutions for the Cauchy problem. | |
| James G. Glimm (SUNY) | Mathematical and numerical principles for turbulent mixing |
| Abstract: Numerical approximation of fluid equations are reviewed. We identify numerical mass diffusion as a characteristic problem in most simulation codes. This fact is illustrated by an analysis of fluid mixing flows. In these flows, numerical mass diffusion has the effect of over regularizing the solution. A number of startling conclusions have recently been observed. For a flow accelerated by multiple shock waves, we observe an interface between the two fluids proportional to Delta x-1, that is occupying a constant fraction of the available mesh degrees of freedom. This result suggests (a) nonconvergence for the unregularized mathematical problem or (b) nonuniqueness of the limit if it exists, or (c) limiting solutions only in the very weak form of a space time dependent probability distribution. The cure for this pathology is a regularized solution, in other words inclusion of all physical regularizing effects, such as viscosity and physical mass diffusion. In other words, the amount of regularization of an unstable flow is of central importance. Too much regularization, with a numerical origin, is bad, and too little, with respect to the physics, is also bad. At the level of numerical modeling, the implication from this insight is to compute solutions of the Navier-Stokes, not the Euler equations. Resolution requirements for realistic problems make this solution impractical in most cases. Thus subgrid transport processes must be modeled, and for this we use dynamic models of the turbulence modeling community. In the process we combine and extend ideas of the capturing community (sharp interfaces or numerically steep gradients) with conventional turbulence models, usually applied to problems relatively smooth at a grid level. The numerical strategy is verified with a careful study of a 2D Richtmyer-Meshkov unstable turbulent mixing problem. We obtain converged solutions for such molecular level mixing quantities as a chemical reaction rate. The strategy is validated (comparison to laboratory experiments) through the study of three dimensional Rayleigh-Taylor unstable flows. | |
| James G. Glimm (SUNY) | Discussion topic: Conservation laws in higher spatial dimensions: Euler vs. Navier-Stokes; theory and computation |
| Abstract: No Abstract | |
| Michael Herty (RWTH Aachen) | Optimal nodal control of networked systems of conservation laws |
| Abstract: In applications of flow in gas and water networks the 1d p-system is used to describe the flow in pipes. The dynamics of each pipe is coupled at a node through coupling conditions inducing boundary conditions. We study the well-posedness of these initial boundary value problems of 2×2 balance laws for a set of general possibly time-dependent coupling conditions. | |
| David Hoff (Indiana University) | Instantaneous boundary-tangency of singularity curves in compressible fluid flow |
| Abstract: We show that, for a model system of compressible fluid flow in the upper half space of the plane, curves which intersect the boundary and across which the initial density is discontinuous become tangent to the boundary instantaneously in time. This result is closely related to the instantaneous formation of cusps in two-dimensional incompressible vortex patches. | |
| Helge Holden (Norwegian University of Science and Technology (NTNU)) | Convergence of operator splitting for the KdV equation |
| Abstract: We consider the KdV equation used for modeling, e.g., water waves in a narrow channel. The time evolution is described by a quadratic (Burgers') plus a linear (Airy) term. Since the evolution of each of these terms is quite different, it is natural to ask whether the concatenation of the evolution operators for each term yields an approximation to the evolution operator for the sum. This strategy has been used with good results when designing numerical methods for the KdV equation, but without rigourous convergence proofs. The aim of this talk is to present a first step in this direction, and show convergence of operator splitting for sufficiently regular initial data. (Joint work with N. H. Risebro, K. H. Karlsen, T. Tao.) | |
| Russell J. Holmes (University of Minnesota) | Organic semiconductors for flexible solar cells |
| Abstract: No Abstract | |
| Xianpeng Hu (University of Pittsburgh), Dehua Wang (University of Pittsburgh) | Global strong solutions to density-dependent viscoelasticity and liquid crystal |
| Abstract: The global strong solutions to the multi-dimensional viscoelastic fluids and liquid crystals are discussed. Here, a strong solution is a solution in W2,q satisfying the equations almost everywhere. | |
| John K. Hunter (University of California, Davis) | Nonlinear surface waves and the loss of uniform Lopatinski stability in IBVPs for hyperbolic conservation laws |
| Abstract: The Kriess-Sakamoto theory for the well-posedness of hyperbolic IBVPs and the Majda theory for shock-wave stability apply under the assumption that a suitable Lopatinski condition holds uniformly. The failure of uniformity is associated with the presence of surface waves on the boundary or discontinuity. We will derive asymptotic equations for "genuine" nonlinear surface waves that decay exponentially away from the surface, such as Rayleigh waves in elasticity or surface waves on a tangential discontinuity in MHD. We will give a short-time existence theorem for smooth solutions of the asymptotic equations under a "tameness" condition on the interaction coefficients between the Fourier components of the surface wave, which prevents the loss of derivatives. We will also show numerical solutions of the asymptotic equations that illustrate singularity formation on the boundary (a mechanism which differs from shock formation in the interior). | |
| Katarina Jegdic (University of Houston-Downtown) | Rarefaction wave interaction for the unsteady transonic small disturbance equation |
| Abstract: We study a Riemann problem for the unsteady transonic small disturbance equation that results in a diverging rarefaction problem. We write the problem in self-similar coordinates and obtain a free boundary value problem with equations that change type (hyperbolic-elliptic). We summarize the main ideas and present the main features of the problem. The flow in the hyperbolic part can be described as a solution of a degenerate Goursat boundary problem, the interaction of the rarefaction wave with the subsonic region is illustrated and the subsonic flow is shown to satisfy a second order degenerate elliptic boundary problem with mixed boundary conditions. This is joint work with Jun Chen and Cleopatra Christoforou (University of Houston). | |
| Helge Kristian Jenssen (Pennsylvania State University) | Symmetric waves for conservation laws |
| Abstract: Motivated by the problem of symmetric collapsing gas-dynamical shocks we present a scalar toy model that captures blowup of focusing waves. This model is simple enough to allow for explicit calculations, and we study some solutions in detail. As a scalar model it does not describe reflection of waves and this necessitates a new concept of weak solutions. Returning to gas-dynamics we review a part of the extensive literature on compressible flow with symmetry, and collapsing shocks in particular. We outline an approach to study possible blowup for collapsing shocks. | |
| Joseph W. Jerome (Northwestern University) | Charge transport in an incompressible fluid medium |
| Abstract: Conservation laws, together with the Gauss law for electrostatics, have been used to model charge transport in solid state semiconductors and in electrolytes for several decades. The determination of the current density is an important aspect of the modeling. In applications to ion channels, and to electrodiffusion more generally, there has been recent interest in the effects of the ambient fluid on current density. We discuss the mathematical model for this case: the Poisson-Nernst-Planck/Navier-Stokes model. The Cauchy problem was investigated by the speaker in [Transport Theory Statist. Phys. 31 (2002), 333--366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for evolution equations. In this talk, the proof of existence of a global distribution solution for the model is discussed, in the case of the initial-boundary value problem. Connection of the above analysis to significant applications is also discussed. | |
| Mathew A. Johnson (Indiana University) | Modulational instability of periodic waves |
| Abstract: Using periodic Evans function expansions, we derive geometric criterion for the modulational instability, i.e. spectral instability to long-wavelength perturbations, of periodic traveling waves of the generalized KdV equation. Such techniques have also recently proven useful for analyzing spectral stability to long-wavelength transverse perturbations, as well as studying nonlinear stability to periodic perturbations. Using standard elliptic function techniques, we can explicitly calculate the necessary geometric information for polynomial nonlinearities: we will only present the results for KdV and modified KdV equations here. This is joint work with Jared. C. Bronski (University of Illinois at Urbana-Champaign). | |
| Barbara Lee Keyfitz (Ohio State University) | The sonic line as a free boundary: Stability under perturbations |
| Abstract: The study of self-similar solutions of multidimensional conservation laws leads to systems of equations that change type. Change of type occurs either across a transonic shock or at a sonic line. Often the sonic line appears as a free boundary in the formulation of the problem. Some recent numerical (and experimental) discoveries of a new kind of shock reflection ('Guderley Mach reflection') lead to interesting and still unresolved questions concerning the nature of the self-similar solutions in this generic case. In this talk, I will present some analysis of a simple model for this phenomenon, using the transonic small disturbance equation. The simplified problem seems amenable to analysis, but we are just beginning to make progress. This is a report on current joint work with Allen Tesdall and Kevin Payne. | |
| Christian F Klingenberg (Bayerische-Julius-Maximilians-Universität Würzburg) | Compressible turbulence modelling in astrophysics |
| Abstract: We present a numerical method for the compressible Euler equations in 3 space dimensions where we combine adaptive mesh refinement with subgrid scale modelling. This increases efficiency and accuracy when computing turbulent flows. We apply this to astrophysical problems. | |
| Philippe G. LeFloch (Université de Paris VI (Pierre et Marie Curie)) | Kinetic relations for undercompressive shocks. Physical, mathematical, and numerical issues |
| Abstract: I will discuss the existence and properties of small-scale dependent shock waves to nonlinear hyperbolic systems, with an emphasis on the theory of nonclassical entropy solutions involving undercompressive shocks. Regularization-sensitive structures often arise in continuum physics, especially in flows of complex fluids or solids. The so-called kinetic relation was introduced for van der Waals fluids and austenite-martensite boundaries (Abeyaratne, Knowles, Truskinovsky) and nonlinear hyperbolic systems (LeFloch) to characterize the correct dynamics of subsonic phase boundaries and undercompressive shocks, respectively. The role of a single entropy inequality is essential for these problems and is tied to the regularization associated with higher-order underlying models –which take into account additional physics and provide a description of small-scale effects. In the last fifteen years, analytical and numerical techniques were developed, beginning with the construction of nonclassical Riemann solvers, which were applied to tackle the initial-value problem via the Glimm scheme. Total variation functionals adapted to nonclassical entropy solutions were constructed. On the other hand, the role of traveling waves in selecting the proper shock dynamics was stressed: traveling wave solutions (to the Navier-Stokes-Korteweg system, for instance) determine the relevant kinetic relation –as well as the relevant family of paths in the context of nonconservative systems. Several physical applications were pursued: (hyperbolic-elliptic) equations of van der Waals fluids, model of thin liquid films, generalized Camassa-Holm equations, etc. Importantly, finite difference schemes with controled dissipation based on the equivalent equation were designed and the corresponding kinetic functions computed numerically. Consequently, `several shock wave theories' are now available to encompass the variety of phenomena observed in complex flows. References: 1993: P.G. LeFloch, Propagating phase boundaries. Formulation of the problem and existence via the Glimm scheme, Arch. Rational Mech. Anal. 123, 153–197. 1997: B.T. Hayes and P.G. LeFloch, Nonclassical shocks and kinetic relations. Scalar conservation laws, Arch. Rational Mech. Anal. 139, 1–56. 2002: P.G. LeFloch, Hyperbolic Systems of Conservation Laws. The theory of classical and nonclassical shock waves, Lectures in Mathematics, ETH Zurich, Birkhauser. 2004: N. Bedjaoui and P.G. LeFloch, Diffusive-dispersive traveling waves and kinetic relations. V. Singular diffusion and dispersion terms, Proc. Royal Soc. Edinburgh 134A, 815–844. 2008: P.G. LeFloch and M. Mohamadian, Why many shock wave theories are necessary. Fourth-order models, kinetic functions, and equivalent equations, J. Comput. Phys. 227, 4162–4189. | |
| Nicholas Matthew Leger (University of Texas) | L2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method |
| Abstract: We consider scalar nonviscous conservation laws with strictly convex flux in one space dimension, and we investigate the behavior of bounded L2 perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L2 norm of a perturbed solution relative to the shock wave is bounded above by the L2 norm of the initial perturbation. | |
| Marta Lewicka (University of Minnesota) | Reduced theories in nonlinear elasticity |
| Abstract: Elastic materials exhibit qualitatively different responses to different kinematic boundary conditions or body forces. As a first step towards understanding the related evolutionary problem, one studies the minimizers of an appropriate nonlinear elastic energy functional. We shall give an overview of recent results, rigorously deriving 2d elasticity theories for thin 3d shells around mid-surfaces of arbitrary geometry. One major ingredient is the study of Sobolev spaces of infinitesimal isometries on surfaces, their density and matching properties. Another one relates to the non-Euclidean version of 3d nonlinear elasticity, conjectured to explain the mechanism for spontaneous formation of non-zero stress equilibria in growing tissues (leaves, flowers). Here, we prove a Gamma-convergence result, and as a corollary, we obtain new conditions for existence of isometric immersions of 2d Riemannian metrics into 3d space. | |
| Tai-Ping Liu (Stanford University) | Kinetic theory and gas dynamics |
| Abstract: The study of shock wave theory for hyperbolic and viscous conservation laws is a good starting point for the study of certain aspects of kinetic theory. It offers different perspective and techniques than those coming from statistical mechanics. The main difference is the emphasis on the fluid dynamical phenomena. However, it is also important to realize that kinetic theory offers more than gas dynamics, particularly when it comes to the shock, initial and boundary layers. Also, depending on the physical situations, different fluid dynamics equations are derived from the Boltzmann equation. We will comment on these issues and present some recent results on invariant manifolds for stationary Boltzmann equation. | |
| Tai-Ping Liu (Stanford University) | Discussion: Kinetic theory and gas dynamics |
| Abstract: No Abstract | |
| Tao Luo (Georgetown University) | Stability of rotating white dwarf stars |
| Abstract: I will present some results on the existence and nonlinear stability for the rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We then apply these results to rotating white dwarf stars to show its dynamical stability when the total mass is less than a critical mass, which is related to the "Chandrasekhar"limit in astrophysics. This is a joint work with Joel Smoller. | |
| Pierangelo Marcati (Università di L'Aquila) | Quantum fluids and related problems |
| Abstract: It will be reviewed briefly various physical models leading to a description based on Quantum Hydrodynamics: Superfluidity, BEC, superconductivity, semiconductors and there will be recalled various derivations of the PDE system. The main result (joint with P. Antonelli) shows the global existence of "irrotational" weak solutions with the sole assumption of finite energy, without any smallness or any further smoothness of the initial data. The approach is based on various tools, namely the wave functions polar decomposition, the construction of approximate solution via a fractional steps method which iterates a Schrödinger Madelung picture with a suitable wave function updating mechanism. Therefore several a priori bounds of energy, dispersive and local smoothing type, allow to prove the compactness of the approximating sequences. A different approach can be used to study small disturbances of subsonic (in the QHD sense) steady states. Some improvements may are shown to be possible in the 2-D analysis. | |
| Nader Masmoudi (New York University) | Global existence for small data water waves |
| Abstract: We prove the global existence of regular solutions to the water waves problem in 3D. The proof is based on the combinaison of energy estimates and dispersive estimates. This is a joint work with Pierre Germain and Jalal Shatah. | |
| Nader Masmoudi (New York University) | Discussion: Free boundary problems related to water waves |
| Abstract: No Abstract | |
| Richard P. McGehee (University of Minnesota) | Modeling the earth's glacial cycles |
| Abstract: No Abstract | |
| Sarka Necasova (Czech Academy of Sciences (AVČR)) | On the motion of several rigid bodies in an incompressible non-Newtonian and heat-conducting fluid |
| Abstract: We will consider the problem of the motion of several rigid bodies in viscous non-Newtonian heat fluid in bounded domain in three dimensional situation.Using penalization method developed by Conca, San Martin, Tucsnak and Starovoitov we have shown the existence of weak solution and moreover we show that for certain non-newtonian fluids there are no collisions among bodie or body and boundary of domain. | |
| Toan Nguyen (Indiana University) | Stability of noncharacteristic viscous boundary layers |
| Abstract: We present our recent results on one- and multi-dimensional asymptotic stability of noncharacteristic boundary layers in gas dynamics (or a more general class of hyperbolic--parabolic systems) with suction- or blowing-type boundary conditions. The linearized and nonlinear stability is established for layers with arbitrary amplitudes, under the assumption of strong spectral, or uniform Evans, stability. The latter assumption has been verified for small-amplitude layers in one-d case by various authors using energy estimates and in multi-d case by Guès, Métivier, Williams, and Zumbrun. For large-amplitude layers, it may be efficiently checked numerically by a combination of asymptotic ODE estimates and numerical Evans function computations. This is a joint work with Kevin Zumbrun. | |
| Duane Nykamp (University of Minnesota) | Toward a second order description of neuronal networks |
| Abstract: No Abstract | |
| Reza Pakzad (University of Pittsburgh) | Elasticity of thin shells and Sobolev spaces of isometries |
| Abstract: We describe the approach through which various elastic shell models are rigorously derived from the 3D nonlinear elasticity theory. Some results and a conjecture on the limiting theories are presented. Spaces of weakly regular isometries or infinitesimal isometries of surfaces arise in this context. Important problems regarding these spaces include rigidity, regularity and density of smooth mappings. This project is partly a collaboration with Marta Lewicka and Maria-Giovanna Mora. | |
| Arshad Ahmud Iqbal Peer (University of Mauritius) | A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws |
| Abstract: We propose a new fourth-order non-oscillatory central scheme for computing approximate solutions of hyperbolic conservation laws. A piecewise cubic polynomial is used for the spatial reconstruction and for the numerical derivatives we choose genuinely fourth-order accurate non-oscillatory approximations. The solution is advanced in time using natural continuous extension of Runge-Kutta methods. Numerical tests on both scalar and gas dynamics problems confirm that the new scheme is non-oscillatory and yields sharp results when solving profiles with discontinuities. Experiments on nonlinear Burgers’ equation indicate that our scheme is superior to existing fourth-order central schemes in the sense that the total variation (TV) of the computed solutions are closer to the total variation of the exact solution. | |
| Benoit Perthame (Université de Paris VI (Pierre et Marie Curie)) | A coupled system of elliptic/conservation law arising in cell self-organization |
| Abstract: Several models have been proposed in order to describe cell communities self-organisation. One of them consists in coupling a multidimensional scalar conservation law with an elliptic equation which gradient determines the flux in the conservation law. In dimension larger than 1, the model looses all nice properties of hyperbolic conservation laws: no contraction property, no BV bound, no regularizing effect. That is the reason why our approach for existence of solutions is based on the kinetic formulation. We recall how weak limits can be handled with this tool and strong convergence follows from uniqueness. In the case at hand, the specific nonlinearity creates an additional defect measure. Fine analysis of properties of this measure provides us with the lacking information to prove uniqueness and deduce that the weak limit still satisfies the system. | |
| Tomasz Piotr Piasecki (Polish Academy of Sciences) | On an inhomogeneous slip-inflow boundary value problem for a steady flow of a viscous compressible fluid in a cylindrical domain |
| Abstract: We investigate a steady flow of a viscous compressible fluid with inflow boundary condition on the density and inhomogeneous slip boundary conditions on the velocity in a cylindrical domain. We show existence of a strong solution that is a small perturbation of a constant flow (v* = (1,0,0), ρ* = 1). We also show that this solution is unique in the class of small perturbations of (v*,ρ*). The nonlinear term in the continuity makes it impossible to apply a fixed point argument. Therefore in order to show the existence of the solution we use a method of successive approximations. | |
| Olga Rozanova (Moscow State University) | The Riemann problem for the stochastically perturbed non-viscous Burgers equation and the pressureless gas dynamics model |
| Abstract: Proceeding from the method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we construct a solution to the Riemann problem for the pressureless gas dynamics and sticky particles system. We analyze the difference in the behavior of discontinuous solution for these two models and relations between them. | |
| Denis Serre (École Normale Supérieure de Lyon) | The nature of viscous dissipation in systems of conservation laws |
| Abstract: In his celebrated thesis, S. Kawashima gave a framework for the analysis of the Cauchy problem for nonlinear viscous systems of conservation laws. Some assumptions are quite natural, while other ones are mysterious and require cumbersome calculations. We clarify the situation, by introducing a set of assumption which is natural and very easy to verify. We derive an existence and uniqueness result of strong solutions, in a slightly larger class than the one known before. | |
| Wen Shen (Pennsylvania State University) | Global BV for a model of granular flow |
| Abstract: We consider a model for the flow of granular matter which was proposed by Hadeler and Kuttler (Granular Matter, 1999). The original model uses the height of the standing layer and the thickness of the moving layer as the unknowns. By introducing the slope the standing layer, one arrives at a 2 by 2 system of balance laws. This system is weakly linearly degenerate at a point. With suitable conditions on the initial data, one can prove the global existence of smooth solutions. Furthermore, we prove the global existence of large BV solutions, for a class of initial data with bounded but possibly large total variation. This is partly a joint work with Debora Amadori, Italy. | |
| Wen Shen (Pennsylvania State University) | Global BV for a model of granular flow |
| Abstract: Same abstract as the talk. | |
| Wen Shen (Pennsylvania State University) | The slow erosion limit in a model of granular flow |
| Abstract: Joint work with Debora Amadori (Università degli Studi dell'Aquila). We study a 2×2 system of balance laws that describes the evolution of a granular material (avalanche) flowing downhill. The original model was proposed by Hadeler and Kuttler. We first consider an initial-boundary value problem, where at the boundary the flow of the incoming material is assigned. For this problem we prove the global existence of BV solutions for a suitable class of data, with bounded by possibly large total variations. We then study the "slow erosion (or deposition) limit", obtained as the thickness of the moving layer tends to zero. We show that, in the limit, the profile of the standing layer depends only on the total mass of the avalanche flowing downhill, not on the time-law describing at which rate the material slides down. More precisely, the limiting slope of the mountain profile is provided by an entropy solution to a scalar integro-differential conservation law. | |
| Chi-Wang Shu (Brown University) | Numerical methods for multi-dimensional systems of conservation laws. Lecture 1 |
| Abstract: In this course we will give an introduction to conservative
short capturing numerical methods for solving multi-dimensional
systems of conservation laws. High order accurate finite
difference, finite volume and discontinuous Galerkin finite
element methods will be covered. We will start with the
basic algorithm issues in a simple scalar one dimensional
setting and then describe the generalization to multi-dimensional
systems. A comparison among these different numerical methods
will be provided.
Lecture References:
[1] C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, B. Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, volume 1697, Springer, Berlin, 1998, pp.325-432. [2] C.-W. Shu, Discontinuous Galerkin methods: general approach and stability, Numerical Solutions of Partial Differential Equations, S. Bertoluzza, S. Falletta, G. Russo and C.-W. Shu, Advanced Courses in Mathematics CRM Barcelona, Birkhäuser, Basel, 2009, pp.149-201. |
|
| Chi-Wang Shu (Brown University) | Numerical methods for multi-dimensional systems of conservation laws. Lecture 2 |
| Abstract: Same abstract as lecture 1. | |
| Chi-Wang Shu (Brown University) | Numerical methods for multi-dimensional systems of conservation laws. Lecture 3 |
| Abstract: Same abstract as lecture 1. | |
| Chi-Wang Shu (Brown University) | Numerical methods for multi-dimensional systems of conservation laws. Lecture 4 |
| Abstract: Same abstract as lecture 1. | |
| Laura Valentina Spinolo (Scuola Normale Superiore) | Well-posedness results for the transport equation, and applications to the chromatography system |
| Abstract: The talk will be based on a joint work with L. Ambrosio, G. Crippa and A. Figalli. First, some new well-posedness results for continuity and transport equations with weakly differentiable velocity fields will be discussed. These results can be applied to the analysis of a 2 x 2 system of conservation laws in one space dimension known as the chromatography system, leading to global existence and uniqueness results for suitable classes of entropy admissible solutions. | |
| Eitan Tadmor (University of Maryland) | Selected topics in approximate solutions of nonlinear conservation laws |
| Abstract: We provide a bird's eye view of a selected topics in approximate solution of nonlinear conservation laws and related time dependent equations. We begin with a discussion on regularity spaces in theory and computation. We will continue with a presentation of the class of high-resolution central schemes. We will discuss the issue of entropy stability and conclude with ongoing research on constrained transport. | |
| Ahmed H. Tewfik (University of Minnesota) | Sparse signal representations and applications |
| Abstract: No Abstract | |
| Lev Truskinovsky (École Polytechnique) | Kinetic relations and beyond |
| Abstract: In this talk we discuss discretization based dispersive-dissipative regularization of mixed type systems and derive the resulting closure conditions known as kinetic relations. Algebraic kinetic relations link velocities of the undercompressed jump discontinuities with the corresponding driving forces and are widely used to model dynamical response of phase boundaries. To capture the effects of discretization more faithfully we propose to replace algebraic kinetic relations with differential kinetic equations which involve some specially selected collective variables characterizing not only the location of the discontinuity but also the structure of the transition region. Joint work with A. Vainchtein. | |
| Athanasios E. Tzavaras (University of Maryland) | Adiabatic shear bands in high strain-rate plasticity |
| Abstract: We consider a system of hyperbolic-parabolic equations describing a material instability mechanism associated to the formation of shear bands at high strain-rate plastic deformations of metals. We consider the case of adiabatic shearing and derive a quantitative criterion for the onset of instability: Using ideas from the theory of relaxation systems we derive equations that describe the effective behavior of the system. The effective equation turns out to be a forward-backward parabolic equation regularized by fourth order term. Further, we study numerically the effect of thermal diffusion on the evolution of these bands. It turns out that while localization initially forms at a later stage of the deformation heat diffusion has the power hinder and even altogether suppress localization and even return the evolution to uniform deformation. (joint work with Th. Katsaounis and Th. Baxevanis, Univ. of Crete). | |
| Athanasios E. Tzavaras (University of Maryland) | Discussion: Conservation laws in elasticity |
| Abstract: No Abstract | |
| Alexis Frederic Vasseur (University of Texas) | Global regularity of solutions to systems of reaction-diffusion with sub-quadratic growth in any dimension |
| Abstract: In this talk, we present the study of the regularity of solutions to some systems of reaction–diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without smallness assumptions, in any dimension N. The proof is based on blow-up techniques. The natural entropy of the system plays a crucial role in the analysis. It allows us to use of De Giorgi type methods introduced for elliptic regularity with rough coefficients. Even if those systems are entropy supercritical, it is possible to control the hypothetical blow-ups, in the critical scaling, via a very weak norm. | |
| Vaughan R. Voller (University of Minnesota) | The development of a similarity solution for a Stefan like problem, with two moving boundaries, related to the growth of a sediment ocean basin |
| Abstract: No Abstract | |
| David H. Wagner (University of Houston) | Elastodynamics, differential forms, and weak solutions |
| Abstract: We offer an alternate derivation for the symmetric-hyperbolic formulation of the equations of motion for a hyperelastic material with polyconvex stored energy. The derivation makes it clear that the expanded system is equivalent, for weak solutions, to the original system. We consider motions with variable as well as constant temperature. In addition, we present equivalent Eulerian equations of motion, which are also symmetric-hyperbolic. | |
| Dehua Wang (University of Pittsburgh) | Transonic flows and isometric embeddings |
| Abstract: Some recent research progresses on the multi-dimensional compressible Euler equations will be reviewed. In particular, the transonic flows past an obstacle such as an airfoil, and the isometric embeddings in geometry will be discussed. The talk is based on the joint works with Gui-Qiang Chen and Marshall Slemrod. | |
| Ya-Guang Wang (Shanghai Jiaotong University) | Stability of multidimensional contact discontinuities in compressible MHD |
| Abstract: In this talk we study the stability of multidimensional contact discontinuities in compressible fluids. There are two kinds of contact discontinuities, one is so-called the vortex sheet, mainly due to that the tangential velocity is discontinuous across the front, and the other one is the entropy wave, for which the velocity is continuous while the entropy has certain jump on the front. It is well-known that the vortex sheet in two dimensional compressible Euler equations is stable when the Mach number is larger than √2, while in three dimensional problem it is always unstable. But, some physical phenomena indicate that the magnetic field has certain stabilization effect for waves in fluids. The first goal of this talk is to rigorously justify this physical phenomenon, and to investigate the stability of three-dimensional current-vortex sheet in compressible magneto-hydrodynamics. By using energy method and the Nash-Moser iteration scheme, we obtain that the current-vortex sheet in three-dimensional compressible MHD is linearly and nonlinearly stable when the magnetic fields on both sides of the front are non-parallel to each other. The second goal is to study the stability of entropy waves. By a simple computation, one can easily observe that the entropy wave is structurally unstable in gas dynamics. By carefully studying the effect of magnetic fields on entropy waves, we obtain that the entropy wave in three-dimensional compressible MHD is stable when the normal mag- netic field is continuous and non-zero on the front. This is a joint work with Gui-Qiang Chen. | |
| Ying Wang (Ohio State University) | Central schemes for a new class of entropy solutions of the modified Buckley-Leverett equation |
| Abstract: Joint work with Chiu-Yen Kao. Buckley-Leverett (BL) equation arises in two-phase flow problem in porous media. It models the oil recovery by water-drive in one-dimension. Here we propose a central scheme for an extension of the BL equation which includes the dynamic effects in the pressure difference between the two phases and results in a third order mixed derivatives term in the modified BL equation. The numerical scheme is able to capture the admissible shocks which is the so-called nonclassical shock due to the violation of the Oleinik entropy condition. | |
| Michael Westdickenberg (Georgia Institute of Technology) | Optimal transport for the system of isentropic Euler equations |
| Abstract: The isentropic Euler equations form a system of conservation laws modeling compressible fluid flows with constant thermodynamical entropy. Due to the occurence of shock discontinuities, the total energy of the system is decreasing in time. We review the second order calculus on the wasserstein space of probability measures and show how the isentropic Euler equations can be interpreted as a steepest descent equation in this framework. We introduce a variational time discretization based on a sequence of minimization problems, and show that this approximation converges to a suitably defined measure-valued solution of the conservation law. Finally, we present some preliminary results about the numerical implementation of our time discretization. | |
| Robin Young (University of Massachusetts) | Strong waves and vaccums in isentropic gas dynamics |
| Abstract: We give a complete description of nonlinear waves and their pairwise interactions in isentropic gas dynamics. Our analysis includes rarefactions, compressions and shock waves. We describe the interaction in terms of a reference state and incident wave strengths, and give explicit estimates of the outgoing wave strengths. Our estimates are global in that they apply to waves of arbitrary strength, and they are uniform in the incoming reference state. In particular, the estimates continue to hold as this state approaches vacuum. We also consider composite interactions, which can be regarded as a degenerate superposition of pairwise interactions. We construct a class of exact weak solutions which demonstrate some interesting and surprising features of interactions, and use these to demonstrate the collapse of a vacuum: in most cases two shocks will emerge from the vacuum, but in certain asymmetric cases a single shock and a rarefaction may emerge. | |
| Robin Young (University of Massachusetts) | Periodic solutions to the Euler equations |
| Abstract: Joint work with Blake Temple. In this ongoing collaboration with Blake Temple, we attempt to prove the existence of periodic solutions to the Euler equations of gas dynamics. Such solutions have long been thought not to exist due to shock formation, and this is confirmed by the celebrated Glimm-Lax decay theory for 2×2 systems. However, in the full 3×3 system, multiple interaction effects can combine to slow down and prevent shock formation. We describe the physical mechanism supporting periodicity, analyze combinatorics of simple wave interactions, and develop periodic solutions to a "linearized" problem. These linearized solutions have a beautiful structure and exhibit several surprising and fascinating phenomena. We then consider perturbing these as a bifurcation problem, which leads us to problems of small divisors and KAM theory. As an intermediate step, we find solutions which are periodic to within arbitrarily high Fourier modes. | |
| Yuxi Zheng (Pennsylvania State University) | Semi-hyperbolic patches of solutions to two-dimensional compressible Euler systems |
| Abstract: We show that there are supersonic solutions to the Euler system that are not hyperbolic in the traditional sense. These solutions occur at the transonic region, whose characteristics may both come from the sonic line and end at the sonic line. Based on the new wave structure, we offer perspectives to construct global transonic solutions to the Riemann problems. | |
| Yuxi Zheng (Pennsylvania State University) | Discussion |
| Abstract: No Abstract | |
| Kevin Zumbrun (Indiana University) | Dynamics of viscous shock waves. Lecture 1: Stability of viscous shock waves |
| Abstract: Course abstract: We examine from a classical dynamical systems point of view stability, dynamics, and bifurcation of viscous shock waves and related solutions of nonlinear pde. Lecture 1 abstract: Stability of viscous shock waves. We discuss the basic types of viscous shock waves, the Evans function condition and its meaning, and outline a basic one-dimensional stability proof assuming that the Evans condition holds. | |
| Kevin Zumbrun (Indiana University) | Dynamics of viscous shock waves. Lecture 2: Verification of the Evans condition |
| Abstract: Using a combination of numerical Evans function computations and asymptotic ODE analysis, we carry out global stability analyses for interesting examples including ideal gas and parallel MHD shocks, across the entire range of physical parameters: in particular, in the large amplitude or magnetic field limit. | |
| Kevin Zumbrun (Indiana University) | Dynamics of viscous shock waves.
Lecture 3: Conditional stability and bifurcation |
| Abstract: Elaborating on the basic stability theory, we examine conditional stability and Hopf bifurcation of possibly unstable viscous shock waves. | |
| Kevin Zumbrun (Indiana University) | Dynamics of viscous shock waves.
Lecture 4: Multi-dimensional dynamics: flow in an infinite cylinder |
| Abstract: We discuss finally stability and bifurcation of flow in a channel with periodic boundary conditions: cellular bifurcation, pattern formation, and an Evans function construction for genuinely multi-dimensional (i.e., nonplanar) solutions. | |
Visitors in Residence
| Luigi Ambrosio | Scuola Normale Superiore | 7/18/2009 - 7/25/2009 |
| Fabio Ancona | Università di Padova | 7/23/2009 - 8/1/2009 |
| Donald G. Aronson | University of Minnesota | 9/1/2002 - 8/31/2009 |
| Myoungjean Bae | University of Wisconsin | 7/12/2009 - 7/31/2009 |
| Santiago Ignacio Betelu | University of North Texas | 7/12/2009 - 7/31/2009 |
| Stefano Bianchini | International School for Advanced Studies (SISSA/ISAS) | 7/22/2009 - 7/29/2009 |
| Brian Bies | Washington University | 6/28/2009 - 8/1/2009 |
| Michael Blaser | Eidgenössische TH Hönggerberg | 7/12/2009 - 8/1/2009 |
| Alberto Bressan | Pennsylvania State University | 7/12/2009 - 7/31/2009 |
| Hannah Callender | University of Minnesota | 9/1/2007 - 8/14/2009 |
| Suncica Canic | University of Houston | 7/29/2009 - 7/31/2009 |
| Gui-Qiang G. Chen | Northwestern University | 7/12/2009 - 7/31/2009 |
| Xianjin Chen | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Bin Cheng | University of Michigan | 7/12/2009 - 7/31/2009 |
| Antoine Choffrut | University of Minnesota | 7/13/2009 - 7/31/2009 |
| Rinaldo Mario Colombo | Università di Brescia | 7/12/2009 - 8/2/2009 |
| Gianluca Crippa | Università di Parma | 7/11/2009 - 8/1/2009 |
| Kathryn Dabbs | University of Tennessee | 6/28/2009 - 7/31/2009 |
| Constantine Dafermos | Brown University | 7/12/2009 - 7/31/2009 |
| Xue Mei Deng | Northwestern University | 7/12/2009 - 7/31/2009 |
| Qian Ding | Northwestern University | 7/12/2009 - 7/31/2009 |
| Liviu Florin Dinu | Romanian Academy of Sciences | 7/12/2009 - 7/27/2009 |
| Marina Ileana Dinu | Polytechnic University of Bucharest | 7/12/2009 - 7/27/2009 |
| Milka Nikolaeva Doktorova | Mount Holyoke College | 6/28/2009 - 7/31/2009 |
| Carlotta Donadello | Northwestern University | 7/12/2009 - 7/31/2009 |
| Olivier Dubois | University of Minnesota | 9/3/2007 - 8/31/2009 |
| Wolf-Patrick Duell | New York University | 7/22/2009 - 7/31/2009 |
| Volker Wilhelm Elling | University of Michigan | 7/12/2009 - 7/31/2009 |
| Nadine Even | Bayerische-Julius-Maximilians-Universität Würzburg | 7/12/2009 - 7/31/2009 |
| Beixiang Fang | Shanghai Jiaotong University | 7/12/2009 - 7/31/2009 |
| Eduard Feireisl | Czech Academy of Sciences (AVČR) | 7/12/2009 - 7/31/2009 |
| Mikhail Feldman | University of Wisconsin | 7/19/2009 - 7/25/2009 |
| Jin Feng | University of Kansas | 7/12/2009 - 7/25/2009 |
| Daniel Flath | Macalester College | 6/29/2009 - 7/31/2009 |
| Hermano Frid | Institute of Pure and Applied Mathematics (IMPA) | 7/12/2009 - 7/31/2009 |
| Frederico C. Furtado | University of Wyoming | 7/13/2009 - 7/24/2009 |
| Shu Gao | Northwestern University | 7/12/2009 - 7/31/2009 |
| Mauro Garavello | Università del Piemonte Orientale "Amedeo Avogadro" | 7/12/2009 - 7/31/2009 |
| James G. Glimm | SUNY | 7/26/2009 - 7/30/2009 |
| Dhruv Goel | University of Minnesota | 6/29/2009 - 7/31/2009 |
| G.D. Veerappa Gowda | Tata Institute of Fundamental Research | 7/12/2009 - 8/1/2009 |
| Graziano Guerra | Università di Milano - Bicocca | 7/11/2009 - 7/31/2009 |
| Arvind Kumar Gupta | Birla Institute of Technology and Science | 7/13/2009 - 7/31/2009 |
| Michael Herty | RWTH Aachen | 7/16/2009 - 7/29/2009 |
| Peter Hinow | University of Minnesota | 9/1/2007 - 8/21/2009 |
| Luan Thach Hoang | Texas Tech University | 7/12/2009 - 8/1/2009 |
| David Hoff | Indiana University | 7/19/2009 - 7/24/2009 |
| Helge Holden | Norwegian University of Science and Technology (NTNU) | 7/12/2009 - 7/26/2009 |
| Russell J. Holmes | University of Minnesota | 7/1/2009 - 7/1/2009 |
| Jingwei Hu | University of Wisconsin | 7/12/2009 - 7/17/2009 |
| Xianpeng Hu | University of Pittsburgh | 7/12/2009 - 7/31/2009 |
| John K. Hunter | University of California, Davis | 7/12/2009 - 7/30/2009 |
| Yunkyong Hyon | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Mark Iwen | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Juhi Jang | Courant Institute of Mathematical Sciences | 7/13/2009 - 7/31/2009 |
| Katarina Jegdic | University of Houston-Downtown | 7/26/2009 - 7/31/2009 |
| Helge Kristian Jenssen | Pennsylvania State University | 7/19/2009 - 7/31/2009 |
| Joseph W. Jerome | Northwestern University | 7/12/2009 - 7/31/2009 |
| Srividhya Jeyaraman | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Lijian Jiang | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Peng Jiang | University of Pittsburgh | 7/12/2009 - 7/31/2009 |
| Mathew A. Johnson | Indiana University | 7/12/2009 - 7/31/2009 |
| Kayyunnapara Thomas Joseph | Tata Institute of Fundamental Research | 7/12/2009 - 8/1/2009 |
| Kenneth Hvistendahl Karlsen | University of Oslo | 7/12/2009 - 7/29/2009 |
| Barbara Lee Keyfitz | Ohio State University | 7/20/2009 - 7/31/2009 |
| Christian F Klingenberg | Bayerische-Julius-Maximilians-Universität Würzburg | 7/15/2009 - 7/30/2009 |
| Alexander Kurganov | Tulane University | 7/12/2009 - 7/31/2009 |
| Bongsuk Kwon | Indiana University | 7/12/2009 - 7/31/2009 |
| Marc Laforest | École Polytechnique de Montréal | 7/12/2009 - 7/20/2009 |
| Chiun-Chang Lee | National Taiwan University | 8/26/2008 - 8/15/2009 |
| Philippe G. LeFloch | Université de Paris VI (Pierre et Marie Curie) | 7/11/2009 - 7/24/2009 |
| Nicholas Matthew Leger | University of Texas | 7/12/2009 - 7/30/2009 |
| Gilad Lerman | University of Minnesota | 6/29/2009 - 7/31/2009 |
| Marta Lewicka | University of Minnesota | 7/13/2009 - 7/31/2009 |
| Lu Li | University of Minnesota | 7/13/2009 - 7/31/2009 |
| Tian-Hong Li | Chinese Academy of Sciences | 7/23/2009 - 7/28/2009 |
| Tong Li | University of Iowa | 7/19/2009 - 7/31/2009 |
| Yachun Li | Shanghai Jiaotong University | 7/12/2009 - 8/1/2009 |
| Yongfeng Li | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Tai-Chia Lin | National Taiwan University | 8/23/2008 - 7/23/2009 |
| Chun Liu | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Hailiang Liu | Iowa State University | 7/12/2009 - 7/15/2009 |
| Tai-Ping Liu | Stanford University | 7/19/2009 - 7/31/2009 |
| Maria Lukacova | Technische Universität Hamburg-Harburg | 7/20/2009 - 8/1/2009 |
| Tao Luo | Georgetown University | 7/25/2009 - 7/31/2009 |
| Pierangelo Marcati | Università di L'Aquila | 7/14/2009 - 7/25/2009 |
| Francesca Marcellini | Università di Milano - Bicocca | 7/11/2009 - 7/31/2009 |
| Dan Marchesin | Instituto de Matematica Pura e Aplicada | 7/14/2009 - 7/23/2009 |
| Vasileios Maroulas | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Andrea Marson | Università di Padova | 7/15/2009 - 7/25/2009 |
| Nader Masmoudi | New York University | 7/19/2009 - 7/31/2009 |
| Richard P. McGehee | University of Minnesota | 7/29/2009 - 7/29/2009 |
| Amelia Ahlers McNamara | Macalester College | 6/28/2009 - 7/31/2009 |
| Michael Meaden | Elmhurst College | 6/28/2009 - 7/31/2009 |
| Francesca Monti | Università di Milano - Bicocca | 7/11/2009 - 7/31/2009 |
| Sarka Necasova | Czech Academy of Sciences (AVČR) | 7/18/2009 - 7/25/2009 |
| Toan Nguyen | Indiana University | 7/12/2009 - 7/25/2009 |
| Truyen V Nguyen | University of Akron | 7/12/2009 - 8/1/2009 |
| Shinya Nishibata | Tokyo Institute of Technology | 7/17/2009 - 8/1/2009 |
| Duane Nykamp | University of Minnesota | 7/8/2009 - 7/8/2009 |
| Reza Pakzad | University of Pittsburgh | 7/12/2009 - 7/31/2009 |
| Ronghua Pan | Georgia Institute of Technology | 7/13/2009 - 7/31/2009 |
| Evgeniy Panov | Novgorod State University | 7/12/2009 - 7/26/2009 |
| Arshad Ahmud Iqbal Peer | University of Mauritius | 7/12/2009 - 8/1/2009 |
| Mikhail Perepelitsa | Vanderbilt University | 7/13/2009 - 7/24/2009 |
| Benoit Perthame | Université de Paris VI (Pierre et Marie Curie) | 7/18/2009 - 7/22/2009 |
| Tomasz Piotr Piasecki | Polish Academy of Sciences | 7/12/2009 - 8/1/2009 |
| Bojan Popov | Texas A & M University | 7/17/2009 - 7/29/2009 |
| Roger Robyr | Universität Zürich | 7/11/2009 - 8/1/2009 |
| Olga Rozanova | Moscow State University | 7/12/2009 - 7/26/2009 |
| Fadil Santosa | University of Minnesota | 7/1/2008 - 6/30/2010 |
| Jordan Richard Seering | University of Minnesota | 6/28/2009 - 7/31/2009 |
| Tsvetanka Sendova | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Denis Serre | École Normale Supérieure de Lyon | 7/18/2009 - 7/31/2009 |
| Michael Shearer | North Carolina State University | 7/14/2009 - 7/24/2009 |
| Wen Shen | Pennsylvania State University | 7/27/2009 - 7/31/2009 |
| Chi-Wang Shu | Brown University | 7/14/2009 - 7/18/2009 |
| Marshall Slemrod | University of Wisconsin | 7/12/2009 - 7/15/2009 |
| Kyungwoo Song | Kyung Hee University | 7/11/2009 - 7/28/2009 |
| Laura Valentina Spinolo | Scuola Normale Superiore | 7/11/2009 - 8/1/2009 |
| Shaowei Su | Northwestern University | 7/12/2009 - 7/31/2009 |
| Eitan Tadmor | University of Maryland | 7/12/2009 - 7/16/2009 |
| Allen Tesdall | College of Staten Island, CUNY | 7/12/2009 - 7/31/2009 |
| Ahmed H. Tewfik | University of Minnesota | 7/15/2009 - 7/15/2009 |
| Monica Torres | Purdue University | 7/12/2009 - 7/26/2009 |
| Konstantina Trivisa | University of Maryland | 7/12/2009 - 7/27/2009 |
| Lev Truskinovsky | École Polytechnique | 7/16/2009 - 8/6/2009 |
| Erkan Tüzel | University of Minnesota | 9/1/2007 - 8/7/2009 |
| Athanasios E. Tzavaras | University of Maryland | 7/14/2009 - 7/29/2009 |
| Alexis Frederic Vasseur | University of Texas | 7/26/2009 - 8/1/2009 |
| Vaughan R. Voller | University of Minnesota | 7/22/2009 - 7/22/2009 |
| David H. Wagner | University of Houston | 7/12/2009 - 7/31/2009 |
| Dehua Wang | University of Pittsburgh | 7/12/2009 - 7/31/2009 |
| Ya-Guang Wang | Shanghai Jiaotong University | 7/15/2009 - 7/31/2009 |
| Ying Wang | Ohio State University | 7/11/2009 - 8/1/2009 |
| Zhian Wang | University of Minnesota | 9/1/2007 - 8/31/2009 |
| Michael Westdickenberg | Georgia Institute of Technology | 7/19/2009 - 7/25/2009 |
| Mark Williams | University of North Carolina | 7/13/2009 - 7/26/2009 |
| Wei Xiong | University of Minnesota | 9/1/2008 - 8/31/2010 |
| Meng Xu | Northwestern University | 7/12/2009 - 7/31/2009 |
| Jue Yan | Iowa State University | 7/12/2009 - 7/15/2009 |
| Hao Ying | Ohio State University | 7/12/2009 - 7/22/2009 |
| Robin Young | University of Massachusetts | 7/12/2009 - 7/24/2009 |
| Matthias Youngs | Indiana University | 7/12/2009 - 7/19/2009 |
| Cheng Yu | Indiana University | 7/12/2009 - 7/31/2009 |
| Haijun Yu | Purdue University | 7/12/2009 - 8/1/2009 |
| Shih-Hsien Yu | National University of Singapore | 7/12/2009 - 7/26/2009 |
| Hairong Yuan | East China Normal University | 7/12/2009 - 7/31/2009 |
| Yanni Zeng | University of Alabama at Birmingham | 7/19/2009 - 8/1/2009 |
| Yi Zeng | University of Illinois at Urbana-Champaign | 6/28/2009 - 7/31/2009 |
| Tianyou Zhang | Pennsylvania State University | 7/13/2009 - 7/28/2009 |
| Yongqian Zhang | Fudan University | 7/20/2009 - 7/31/2009 |
| Kun Zhao | Georgia Institute of Technology | 7/12/2009 - 7/28/2009 |
| Yuxi Zheng | Pennsylvania State University | 7/20/2009 - 7/28/2009 |
| Weigang Zhong | University of Minnesota | 9/8/2008 - 8/31/2010 |
| Dianwen Zhu | University of California, Davis | 7/12/2009 - 7/31/2009 |
| Hao Zou | Macalester College | 6/28/2009 - 7/31/2009 |
| Kevin Zumbrun | Indiana University | 7/12/2009 - 7/22/2009 |
Legend:
Postdoc or Industrial Postdoc
Long-term Visitor
IMA Affiliates:
Arizona State University, Boeing, Corning Incorporated, ExxonMobil, Ford, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Kent State University, Korea Advanced Institute of Science and Technology (KAIST), Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Microsoft Research, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger Cambridge Research, Schlumberger-Doll, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Tennessee, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute