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Local energy decay of solutions to the wave equation for nontrapping metrics

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Arkiv för Matematik

Abstract

We prove uniform local energy decay estimates of solutions to the wave equation on unbounded Riemannian manifolds with nontrapping metrics. These estimates are derived from the properties of the resolvent at high frequency. Applications to a class of asymptotically Euclidean manifolds as well as to perturbations by non-negative long-range potentials are given.

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Authors and Affiliations

  1. Département de Mathématiques UMR 6629 du CNRS, Université de Nantes, 2, rue de la Houssinière, BP 92208, FR-44322, Nantes Cedex 03, France

    Georgi Vodev

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  1. Georgi Vodev
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Vodev, G. Local energy decay of solutions to the wave equation for nontrapping metrics. Ark. Mat. 42, 379–397 (2004). https://doi.org/10.1007/BF02385487

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  • DOI: https://doi.org/10.1007/BF02385487

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