DECAY OF SOLUTIONS OF THE WAVE EQUATION WITH LOCALIZED NONLINEAR DAMPING AND TRAPPED RAYS

被引：4
|
作者：
Phung, Kim Dang [1 ]
机构：
[1] Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China
来源：
MATHEMATICAL CONTROL AND RELATED FIELDS | 2011年 / 1卷 / 02期
关键词：
Wave equation; decay estimates; localized nonlinear damping; trapped rays;
D O I：
10.3934/mcrf.2011.1.251
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove some decay estimates of the energy of the wave equation governed by localized nonlinear dissipations in a bounded domain in which trapped rays may occur. The approach is based on a comparison with the linear damped wave equation and an interpolation argument. Our result extends to the nonlinear damped wave equation the well-known optimal logarithmic decay rate for the linear damped wave equation with regular initial data.
引用
收藏
页码：251 / 265
页数：15
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