# PDEs

Thursday, November 12, 2015 - 11:00am - 12:00pm

Sergei Avdonin (University of Alaska)

We consider control and inverse problems on metric graphs for several

types of PDEs including

the wave, heat and Schr\odinger equations. We demonstrate that, for

graphs without cycles,

unknown coefficients of the equations together with the topology of the

graph and lengths of the edges

can be recovered from the dynamical Dirichlet-to-Neumann map associated

to the boundary vertices.

For general graphs with cycles additional observations at the internal

vertices are needed for stable identification.

types of PDEs including

the wave, heat and Schr\odinger equations. We demonstrate that, for

graphs without cycles,

unknown coefficients of the equations together with the topology of the

graph and lengths of the edges

can be recovered from the dynamical Dirichlet-to-Neumann map associated

to the boundary vertices.

For general graphs with cycles additional observations at the internal

vertices are needed for stable identification.

Wednesday, August 5, 2009 - 11:20am - 11:40am

Robert Shuttleworth (ExxonMobil)

Wednesday, June 5, 2013 - 3:30pm - 4:00pm

David Uminsky (University of San Francisco)

We present an overview of recent results on localized pattern formation in non-local PDEs that arise in swarming and self-assembly models. Much work has been done in one dimension but two dimensions and higher has been more challenging. We present a mathematical framwork which predicts the rich array of localized patterns which have been observed in two and three dimensions. In particular we compute the non-local, linear stability analysis for particles which bifurcate away from radially symmetric states such as rings and spheres.

Tuesday, June 4, 2013 - 1:30pm - 2:00pm

Jean-Philippe Lessard (Laval University)

In this talk, we introduce a rigorous computational method for periodic orbits of dissipative PDEs. The idea is to consider a space-time Fourier expansion of a periodic solution and to solve for its Fourier coefficients in a space of algebraically decaying sequences. The rigorous computation is based on the radii polynomials approach, which provide an efficient means of constructing a ball centered at a numerical approximation which contains a genuine periodic solution.

Thursday, January 17, 2013 - 11:30am - 12:20pm

James Nolen (Duke University)

I will talk about solutions to an elliptic PDE with conductivity coefficient that varies randomly with respect to the spatial variable. It has been known for some time that homogenization may occur when the coefficients are scaled suitably. Less is known about fluctuations of the solution around its mean behavior. For example, if an electric potential is imposed at the boundary, some current will flow through the material. What is the net current? For a finite random sample of the material, this quantity is random.

Monday, December 3, 2012 - 9:00am - 9:50am

Stanley Osher (University of California, Los Angeles)

We review work with Guy Gilboa on the use of nonlocal operators to

define new types of functionals for image processing and elsewhere. This

gives an advantage in handling textures and repetitive structures.

then we will discuss new joint work with Hayden Schaeffer, Russle Caflisch

and Cory Hauck on sparse solvers for multiscale PDE. we seem to automatically very efficiently represent the dynamics of multiscale PDE's

including Navier-Stokes equation, with a very simple sparsification idea.

define new types of functionals for image processing and elsewhere. This

gives an advantage in handling textures and repetitive structures.

then we will discuss new joint work with Hayden Schaeffer, Russle Caflisch

and Cory Hauck on sparse solvers for multiscale PDE. we seem to automatically very efficiently represent the dynamics of multiscale PDE's

including Navier-Stokes equation, with a very simple sparsification idea.

Friday, September 21, 2012 - 1:00pm - 2:30pm

Chongchun Zeng (Georgia Institute of Technology)

Thursday, September 20, 2012 - 11:00am - 12:30pm

Chongchun Zeng (Georgia Institute of Technology)

Wednesday, September 19, 2012 - 1:00pm - 2:30pm

Chongchun Zeng (Georgia Institute of Technology)

Invariant manifolds and foliations have become very useful tools in

dynamical systems. For infinite dimensional systems generated by

evolutionary PDEs, the mere existence of these structures is

non-trivial compared to those of ODEs due to issues such as the

non-existence of backward (in time) solutions of some PDEs or

nonlinear terms causing derivative losses. In addition to systematic

generalization of the standard theory, often specific treatment has to

dynamical systems. For infinite dimensional systems generated by

evolutionary PDEs, the mere existence of these structures is

non-trivial compared to those of ODEs due to issues such as the

non-existence of backward (in time) solutions of some PDEs or

nonlinear terms causing derivative losses. In addition to systematic

generalization of the standard theory, often specific treatment has to

Tuesday, October 19, 2010 - 8:30am - 9:30am

Andrew Majda (New York University)

This lecture is based on the following papers: 1. A. Majda and B.

Gershgorin, 2010: Quantifying Uncertainty in Climate Change Science

Through Empirical Information Theory, PNAS in press 2. A. Majda, R.

Abramov, B. Gershgorin, High Skill in Low Frequency Climate Response

through Fluctuation Dissipation Theorems Despite Structural

Instability, PNAS, January 2010, Vol. 107, no. 2, pp 581 - 586. 3. B.

Gershgorin, A. Majda, Filtering A Nonlinear Slow-Fast System with

Gershgorin, 2010: Quantifying Uncertainty in Climate Change Science

Through Empirical Information Theory, PNAS in press 2. A. Majda, R.

Abramov, B. Gershgorin, High Skill in Low Frequency Climate Response

through Fluctuation Dissipation Theorems Despite Structural

Instability, PNAS, January 2010, Vol. 107, no. 2, pp 581 - 586. 3. B.

Gershgorin, A. Majda, Filtering A Nonlinear Slow-Fast System with