Optimal decay rate for the wave equation on a square with constant damping on a strip
Mathematical Physics
2017-03-03 v2 Analysis of PDEs
math.MP
Abstract
We consider the damped wave equation with Dirichlet boundary conditions on the unit square. We assume the damping to be a characteristic function of a strip. We prove the exact -decay rate for the energy of classical solutions. This answers a question of Anantharaman and L\'eautaud (2014).
Keywords
Cite
@article{arxiv.1607.03633,
title = {Optimal decay rate for the wave equation on a square with constant damping on a strip},
author = {Reinhard Stahn},
journal= {arXiv preprint arXiv:1607.03633},
year = {2017}
}
Comments
10 pages. In version 2 we corrected a minor mistake in the formulation of Theorem 1. A slightly extended and revised version of the paper will be published in the "Zeitschrift f\"ur angewandte Mathematik und Physik" in April 2017 (online 15th of February)