Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle

Abstract

Consider the mixed problem with Dirichelet condition associated to the wave equation ∂ ²_t  u − div_x(É‘(t, x)∇_x u) = 0, where the scalar metric É‘(t, x) is T-periodic in t and uniformly equal to 1 outside a compact set in x, on a T-periodic domain. Let ð˜œ(t, 0) be the associated propagator. Assuming that the perturbations are non-trapping, we prove the meromorphic continuation of the cut-off resolvent of the Floquet operator ð˜œ(T, 0) and we establish sufficient conditions for local energy decay.