Dispersion for the wave equation inside strictly convex domains I: The Friedlander model case

Abstract

We consider a model case for a strictly convex domain Ω ⊂ Rd of dimension d ≥ 2 with smooth boundary ∂Ω ≠ 0, and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay rate for the smoothed out Green function: a t1/4 loss occurs with respect to the boundary less case, due to repeated occurrences of swallowtail type singularities in the wave front set. © 2014 Oana Ivanovici, Gilles Lebeau, Fabrice Planchon.