University of Cambridge > Talks.cam > Partial Differential Equations seminar > Dispersive estimates for the wave equation in strictly convex domains

Dispersive estimates for the wave equation in strictly convex domains

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact .

In recent years, following results on dispersive estimates for low regularity metrics, substantial progress has been made on dispersive estimates for the wave and Schrodinger equations on domains. Here we report on recent work to obtain a sharp dispersion estimate. For this, we rely on a precise description of the wave front (or the pseudo-spheres, e.g. surfaces reached by light emanating from a point after a fixed amount of time) and on a suitable microlocal parametrix construction near the boundary, for the wave equation inside strictly convex domains, subject to Dirichlet boundary condition. Such a parametrix allows to follow wave packets propagating along the boundary with a large number of reflections. In the process we encounter Fourier Integral Operators whose canonical forms correspond to cusp and swallowtail singularities, and which account for the loss (compared to the boundary less case) in dispersive estimates. This is joint work with Gilles Lebeau and Fabrice Planchon.

This talk is part of the Partial Differential Equations seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity