On the stochastic wave equation with nonlinear damping

被引：24

作者：

Kim, Jong Uhn ^{[1
]}

机构：

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2008年 / 58卷 / 01期

关键词：

wave equation; nonlinear damping; initial boundary value problem; Brownian motion; invariant measure;

D O I：

10.1007/s00245-007-9029-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping.

引用

页码：29 / 67

页数：39

共 50 条

[1] On the Stochastic Wave Equation with Nonlinear Damping
Jong Uhn Kim
Applied Mathematics and Optimization, 2008, 58 : 29 - 67
[2] Global attractors for the wave equation with nonlinear damping
Sun, Chunyou
Yang, Meihua
Zhong, Chengkui
JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 227 (02) : 427 - 443
[3] On the dimension of the attractor for the wave equation with nonlinear damping
Prazak, D
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2005, 4 (01) : 165 - 174
[4] Global existence and explosive solution for stochastic viscoelastic wave equation with nonlinear damping
Liang, Fei
Gao, Hongjun
REVIEWS IN MATHEMATICAL PHYSICS, 2014, 26 (07)
[5] Fractal dimension of attractors for a stochastic wave equation with nonlinear damping and white noise
Fan, Xiaoming
Wang, Yaguang
STOCHASTIC ANALYSIS AND APPLICATIONS, 2007, 25 (02) : 381 - 396
[6] Strong Convergence Rates for a Full Discretization of Stochastic Wave Equation with Nonlinear Damping
Cai, Meng
Cohen, David
Wang, Xiaojie
JOURNAL OF SCIENTIFIC COMPUTING, 2025, 102 (02)
[7] Regularity and scattering for the wave equation with a critical nonlinear damping
Todorova, Grozdena
Ugurlu, Davut
Yordanov, Borislav
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2009, 61 (02) : 625 - 649
[8] Decay of solutions of the wave equation with arbitrary localized nonlinear damping
Bellassoued, M
JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 211 (02) : 303 - 332
[9] Stabilization of the wave equation with localized nonlinear damping
Tebou, LRT
JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 145 (02) : 502 - 524
[10] The stochastic nonlinear damped wave equation
Barbu, V
Da Prato, G
APPLIED MATHEMATICS AND OPTIMIZATION, 2002, 46 (2-3) : 125 - 141

← 1 2 3 4 5 →