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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

October 28, 2015 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Oana Ivanovici (Sorbonne University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract

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).

 

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