Local energy decay for several evolution equations on asymptotically euclidean manifolds

Details Local energy decay for several evolution equations on asymptotically euclidean manifolds Local energy decay for several evolution equations on asymptotically euclidean manifolds

2010-08-13

arxiv.org/abs/1008.2357v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

Let P be a long range metric perturbation of the Euclidean Laplacian on R^d, d>1. We prove local energy decay for the solutions of the wave, Klein-Gordon and Schroedinger equations associated to P. The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group exp(itf(P)) where f has a suitable development at zero (resp. infinity).

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