Decay for the Kelvin-Voigt damped wave equation: Piecewise smooth damping
Analysis of PDEs
2021-12-21 v2 Optimization and Control
Abstract
We study the energy decay rate of the Kelvin-Voigt damped wave equation with piecewise smooth damping on the multi-dimensional domain. Under suitable geometric assumptions on the support of the damping, we obtain the optimal polynomial decay rate which turns out to be different from the one-dimensional case studied in \cite{LR05}. This optimal decay rate is saturated by high energy quasi-modes localised on geometric optics rays which hit the interface along non orthogonal neither tangential directions. The proof uses semi-classical analysis of boundary value problems.
Keywords
Cite
@article{arxiv.2007.12994,
title = {Decay for the Kelvin-Voigt damped wave equation: Piecewise smooth damping},
author = {Nicolas Burq and Chenmin Sun},
journal= {arXiv preprint arXiv:2007.12994},
year = {2021}
}
Comments
33 pages, 3 figures