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

摘要

Consider the mixed problem with Dirichelet condition associated to the wave equation , where the scalar metric periodic in t and uniformly equal to 1 outside a compact set in x, on a T-periodic domain. Let 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 and we establish sufficient conditions for local energy decay.