Consider the mixed problem with Dirichelet condition associated to the wave equation ∂ 2t u − divx(ɑ(t, x)∇x u) = 0, where the scalar metric ɑ(t, x) is T-periodic in t and uniformly equal to 1 outside a compact set in x, on a T-periodic domain. Let 𝘜(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 𝘜(T, 0) and we establish sufficient conditions for local energy decay.
@article{1346, title = {Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle}, journal = {CUBO, A Mathematical Journal}, volume = {14}, year = {2012}, language = {en}, url = {http://dml.mathdoc.fr/item/1346} }
Kian, Yavar. Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle. CUBO, A Mathematical Journal, Tome 14 (2012) . http://gdmltest.u-ga.fr/item/1346/