Energy decay for the time dependent damped wave equation
Analysis of PDEs
2023-11-14 v4 Mathematical Physics
math.MP
Optimization and Control
Abstract
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions decays at an exponential rate if the damping coefficient satisfies a time dependent analogue of the classical geometric control condition. Existing time dependent observability inequalities are improved by removing technical assumptions on the permitted initial data.
Cite
@article{arxiv.2207.06260,
title = {Energy decay for the time dependent damped wave equation},
author = {Perry Kleinhenz},
journal= {arXiv preprint arXiv:2207.06260},
year = {2023}
}
Comments
18 pages. This new version corrects some typos and better clarifies in Remark 2 why the technical improvements to the observability inequalities are not trivial consequences of existing results