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

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DOI:

https://doi.org/10.4067/s0719-06462012000200008

Abstract

Consider the mixed problem with Dirichelet condition associated to the wave equation ∂ 2t  u − divx(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.

Keywords

time-dependent perturbation , moving obstacle , local energy decay , wave equation
  • Yavar Kian Centre de Physique Th´eorique CNRS-Luminy, Case 907, 13288 Marseille, France.
  • Pages: 153–173
  • Date Published: 2012-06-01
  • Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal

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Published

2012-06-01

How to Cite

[1]
Y. Kian, “Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle”, CUBO, vol. 14, no. 2, pp. 153–173, Jun. 2012.

Issue

Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal

Section

Articles