PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Tianyou Zhang.

Title:Lipschitz metrics for a class of nonlinear wave equations
Seminar:Hyperbolic and Mixed Type PDEs Seminar
Speaker:Alberto Bressan, Penn State
For conservative solutions to the variational wave equation u_tt - c(u) (c(u) u_x)_x = 0 the energy is a.e. constant. This yields an easy a priori bound on the H^1 norm of a solution. However, the H^1 distance between two solutions at any time t > 0 cannot be controlled by the H^1 distance at time t = 0. Detailed estimates on the dependence on initial data can be formally obtained in terms of a "geodesic distance", related to the cost of an optimal transportation problem. In this talk, after a general introduction on Lipschitz metrics for non-smooth evolutions, I shall discuss how to construct such a geodesic distance, relying on the fact that "generic solutions" of this wave equation are piecewise regular.

Room Reservation Information

Room Number:MB216
Date:09 / 25 / 2014
Time:10:00am - 10:50am