Dispersion for the wave and the Schrödinger equations outside strictly convex domains
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: MSRI: Simons Auditorium
We consider a (general) strictly convex domain in R^d of dimension d>1 and we describe dispersion for both wave and Schrödinger equations with Dirichlet boundary condition. If d=2 or d=3 we show that dispersion does hold like in the flat case, while for d>3, we show that there exist strictly convex obstacles for which a loss occur with respect to the boundary less case (such an optimal loss is obtained by explicit computations).