Local Energy Decay and Diffusive Phenomenon in a Dissipative Wave Guide
Mathematical Physics
2016-01-21 v1 math.MP
Abstract
We prove the local energy decay for the wave equation in a wave guide with dissipation at the boundary. It appears that for large times the dissipated wave behaves like a solution of a heat equation in the unbounded directions. The proof is based on resolvent estimates. Since the eigenvectors for the transverse operator do not form a Riesz basis, the spectral analysis does not trivially reduce to separate analyses on compact and Euclidean domains.
Cite
@article{arxiv.1601.05299,
title = {Local Energy Decay and Diffusive Phenomenon in a Dissipative Wave Guide},
author = {Julien Royer},
journal= {arXiv preprint arXiv:1601.05299},
year = {2016}
}