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 |

Abstract: |

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 |