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

2011/07/26 by Bony, Jean-Francois, Dietrich Häfner, Hafner, Dietrich
Engineering · Mathematics · #35L05 #35P25 #47A10 #58J45 #81U30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1107.5251

openalex publication_date 2011/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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