Optimal decay rate for the wave equation on a square with constant damping on a strip
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- 作者：Reinhard Stahn
- 关键词：Damped wave equation ; Piecewise constant damping ; Energy ; Resolvent estimates ; Polynomial decay ; \(C_0\) ; semigroups
- 刊名：Zeitschrift für angewandte Mathematik und Physik
- 出版年：2017
- 出版时间：April 2017
- 年：2017
- 卷：68
- 期：2
- 全文大小：
- 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
- 出版者：Springer International Publishing
- ISSN：1420-9039
- 卷排序：68
文摘
We consider the damped wave equation with Dirichlet boundary conditions on the unit square parametrized by Cartesian coordinates x and y. We assume the damping a to be strictly positive and constant for \(x<\sigma \) and zero for \(x>\sigma \). We prove the exact \(t^{-4/3}\)-decay rate for the energy of classical solutions. Our main result (Theorem 1) answers question (1) of Anantharaman and Léautaud (Anal PDE 7(1):159–214, 2014, Section 2C).