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

Abstract

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

References in corpus (1)

• Semiclassical scattering amplitude at the maximum point of the potential

Cited by in corpus (2)

• Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space
• The wave equation on asymptotically de Sitter-like spaces