Campuses:

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.
Wednesday, August 5, 2009 - 11:20am - 11:40am
Robert Shuttleworth (ExxonMobil)


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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.
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
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
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