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
|Date:||09 / 25 / 2014|
|Time:||10:00am - 10:50am|