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

页码：251 / 265

页数：15

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