THIS LECTURE HAS BEEN CANCELLED The Weizmann Institute of Science Faculty of Mathematics and Computer Science Mathematical Analysis and Applications Seminar Lecture Hall, Room 1, Ziskind Building CANCELLED ((((on Tuesday, April 23, 2013)))) ((((11:00 - noon)))) Richard Lascar Universit\'e Pierre and Marie Curie, Paris, France will speak on Dispersion for the Wave Equation Inside Strictly Convex Domains Abstract: We consider a strictly convex domain with non empty smooth boundary and of dimension greater than one. We describe dispersion estimates for the wave equation with Dirichlet boundary conditions. We obtain the optimal fixed time decay rate for the smoothed out Green function: a $t^{1/4}$ loss occurs with respect to the boundary less case, due to repeated occurrences of swallowtail types singularities in the wave front set. The study of the model case, i.e. the Friedlander model, has been achieved in August 2012 by O. Ivanovici, G. Lebeau and F. Planchon. In this lecture we shall try to discuss the general case for strictly convex domains, reading carefully the famous result of Melrose about equivalence of glancing hypersurfaces, and the results of Taylor- Melrose- Eskin about microlocal parametrices. The main tools are the geometric constructions of G. Lebeau allowing suitable solutions of the iconal equations. A consequence is the so-called Strichartz estimates for the wave equation inside strictly convex domains with smooth boundaries. The main application is the existence of global solutions for non linear critical wave equations though the dispersion presents its own interest. Joint work with O. Ivanovici, G. Lebeau, F. Planchon. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>