PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Toan Nguyen, Fei Wang, Hope Shaffer, Mark Levi, Victor Nistor, Jinchao Xu.

Title:Rigorous justification of formal multiscale expansions describing wave propagation
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Mark Williams, University of North Carolina at Chapel Hill
Abstract Link:
Formal multiscale expansions have been used for a long time in efforts to understand the qualitative properties of solutions to hyperbolic systems (waves). The question of whether approximate solutions given by such expansions are close to true exact solutions is an interesting and difficult mathematical problem. In the 1950s Peter Lax provided one of the first rigorous justifications in the linear case. In a series of papers in the 1990s Joly, Metivier, and Rauch provided the first rigorous treatment of the nonlinear case for problems in free space (no boundaries). We will review some of this background and then discuss some recent progress on problems involving free or fixed boundaries. The luncheon seminar will provide some background on the construction of formal approximate multiscale solutions, and the CAM Colloquium will discuss methods for showing that such approximate solutions are close to true exact solutions. The talks will be given with chalk, and every effort will be made to make them understandable to graduate students.

Room Reservation Information

Room Number:MB106
Date:10 / 28 / 2013
Time:02:30pm - 03:30pm