Decay and non-decay of the local energy for the wave equation in the De Sitter - Schwarzschild metric

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We describe an expansion of the solution of the wave equation in the De Sitter - Schwarzschild metric in terms of resonances. The main term in the expansion is due to a zero resonance. The error term decays polynomially if we permit a logarithmic derivative loss in the angular directions and exponentially if we permit an small derivative loss in the angular directions.
22 pages, 5 figures

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Analysis of PDEs, Mathematical Physics, 35B34; 35P25; 35Q75; 83C57

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http://salesiana.dossiersoluciones.com/handle/123456789/129792

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.0350
 http://arxiv.org/abs/0706.0350

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arXiv