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

共 50 条

[21] Energy decay rates for solutions of the wave equation with boundary damping and source term
Jong Yeoul Park
Tae Gab Ha
Yong Han Kang
Zeitschrift für angewandte Mathematik und Physik, 2010, 61 : 235 - 265
[22] Energy decay rates for solutions of the wave equation with boundary damping and source term
Park, Jong Yeoul
Ha, Tae Gab
Kang, Yong Han
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2010, 61 (02): : 235 - 265
[23] Localized solutions of the wave equation
Lekner, John
WAVE MOTION, 2025, 132
[24] Energy decay rates for solutions of the wave equations with nonlinear damping in exterior domain
Daoulatli, M.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (07) : 4260 - 4302
[25] Energy decay for wave equations with a potential and a localized damping
Xiaoyan Li
Ryo Ikehata
Nonlinear Differential Equations and Applications NoDEA, 2024, 31
[26] Energy decay for wave equations with a potential and a localized damping
Li, Xiaoyan
Ikehata, Ryo
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (02):
[27] On the stochastic wave equation with nonlinear damping
Kim, Jong Uhn
APPLIED MATHEMATICS AND OPTIMIZATION, 2008, 58 (01) : 29 - 67
[28] Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term
Cavalcanti, MM
Cavalcanti, VND
Martinez, P
JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 203 (01) : 119 - 158
[29] On the Stochastic Wave Equation with Nonlinear Damping
Jong Uhn Kim
Applied Mathematics and Optimization, 2008, 58 : 29 - 67
[30] GLOBAL EXISTENCE AND DECAY OF ENERGY FOR A NONLINEAR WAVE EQUATION WITH p-LAPLACIAN DAMPING
Rammaha, Mohammad
Toundykov, Daniel
Wilstein, Zahava
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (12) : 4361 - 4390

← 1 2 3 4 5 →