Communications in Mathematical Physics

, Volume 282, Issue 3, pp 697–719 | Cite as

Decay and Non-Decay of the Local Energy for the Wave Equation on the De Sitter–Schwarzschild Metric

Article

Abstract

We describe an expansion of the solution of the wave equation on the De Sitter–Schwarzschild metric in terms of resonances. The principal term in the expansion is due to a resonance at 0. The error term decays polynomially if we permit a logarithmic derivative loss in the angular directions and exponentially if we permit an \({\varepsilon}\) derivative loss in the angular directions.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut de Mathématiques de Bordeaux, UMR 5251 du CNRS, Université de Bordeaux ITalence cedexFrance

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