Local decay for the damped wave equation in the energy space

Julien Royer (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We improve a previous result about the local energy decay for the damped wave equation on R^d. The problem is governed by a Laplacian associated with a long range perturbation of the flat metric and a short range absorption index. Our purpose is to recover the decay O(t^{−d+ε}) in the weighted energy spaces. The proof is based on uniform resolvent estimates, given by an improved version of the dissipative Mourre theory. In particular we have to prove the limiting absorption principle for the powers of the resolvent with inserted weights.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Julien Royer. Local decay for the damped wave equation in the energy space. Journal of the Institute of Mathematics of Jussieu, 2018, 17 (3). ⟨hal-01158244⟩