Equation des ondes amorties dans un domaine exterieur

摘要

We study the position of diffusion poles for the Dirichlet problem for the dissipative wave equation in the exterior of an aribitrary obstacle in R~d. We deduce under the "Exterior Geometric Control" condition the behavior of the solutions for large time. We give, in particular, a formula for the best rate of decay of the local energy in odd dimension spaces.