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

[41] General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms
Boulaaras, Salah
Kamache, Fares
Bouizem, Youcef
Guefaifia, Rafik
BOUNDARY VALUE PROBLEMS, 2020, 2020 (01)
[42] DECAY OF SOLUTIONS OF THE WAVE-EQUATION WITH NONLINEAR BOUNDARY FEEDBACK
CONRAD, F
RAO, BP
LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, 1993, 185 : 512 - 523
[43] DECAY AND SCATTERING OF SOLUTIONS OF A NONLINEAR RELATIVISTIC WAVE-EQUATION
MORAWETZ, CS
STRAUSS, WA
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1972, 25 (01) : 1 - &
[44] EXPONENTIAL DECAY FOR THE SEMILINEAR WAVE-EQUATION WITH LOCALIZED DAMPING IN UNBOUNDED-DOMAINS
ZUAZUA, E
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1991, 70 (04): : 513 - 529
[45] STABILIZATION OF SOLUTIONS TO HIGHER-ORDER NONLINEAR SCHRODINGER EQUATION WITH LOCALIZED DAMPING
Bisognin, Eleni
Bisognin, Vanilde
Vera Villagran, Octavio Paulo
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
[46] Local energy decay for the wave equation with a nonlinear time-dependent damping
Bchatnia, Ahmed
Daoulatli, Moez
APPLICABLE ANALYSIS, 2013, 92 (11) : 2288 - 2308
[47] 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
[48] ENERGY DECAY RATES FOR SOLUTIONS OF THE WAVE EQUATION WITH LINEAR DAMPING IN EXTERIOR DOMAIN
Daoulatli, Moez
EVOLUTION EQUATIONS AND CONTROL THEORY, 2016, 5 (01): : 37 - 59
[49] 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
[50] Localized solutions of the wave equation
Lekner, John
WAVE MOTION, 2025, 132

← 1 2 3 4 5 →