Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Sobajima, Motohiro¹  Wakasugi, Yuta² 

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 1628601, Japan

[2] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furocho, Nagoya, Aichi 4648602, Japan

关键词: Damped wave equation;    Diffusion phenomena;    Friedrichs extensions;    Semigroup estimates;    Weighted energy estimates;   

DOI  :  10.1016/j.jde.2016.08.006

来源: Elsevier

【 摘 要 】

In this paper, we consider the asymptotic behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We prove that when the damping is effective, the solution is approximated by that of the corresponding heat equation as time tends to infinity. Our proof is based on semigroup estimates for the corresponding heat equation and weighted energy estimates for the damped wave equation. The optimality of the decay late for solutions is also established. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free