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Improved local energy decay for the wave equation on asymptotically Euclidean odd dimensional manifolds in the short range case

Part of: Hyperbolic equations and systems Partial differential equations on manifolds; differential operators General theory of linear operators Scattering theory Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  13 July 2012

Jean-François Bony  and
Dietrich Häfner
Jean-François Bony
Affiliation:
Institut de Mathématiques de Bordeaux, UMR 5251 du CNRS, Université de Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France ([email protected])
Dietrich Häfner
Affiliation:
Université de Grenoble 1, Institut Fourier, UMR 5582 du CNRS, BP 74, 38402 St Martin d’Hères, France ([email protected])
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Abstract

We show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the metric towards the Euclidean metric. We also give estimates of powers of the resolvent of the wave propagator between weighted spaces.

Keywords

local energy decayresolvent smoothnesswave equationodd dimensionslow frequenciesasymptotically Euclidean manifolds

MSC classification

Secondary: 35L05: Wave equation 35P25: Scattering theory 47A10: Spectrum, resolvent 58J45: Hyperbolic equations 81U30: Dispersion theory, dispersion relations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 3 , July 2013 , pp. 635 - 650
Copyright
©Cambridge University Press 2012 

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