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

[31] DECAY OF SOLUTIONS OF THE WAVE EQUATION WITH LOCALIZED NONLINEAR DAMPING AND TRAPPED RAYS
Phung, Kim Dang
MATHEMATICAL CONTROL AND RELATED FIELDS, 2011, 1 (02) : 251 - 265
[32] Stability of wave equation with locally viscoelastic damping and nonlinear boundary source
Hao, Jianghao
Lv, Mengxian
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 490 (01)
[33] Rate of decay of solutions of the wave equation with arbitrary localized nonlinear damping
Daoulatli, M.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (04) : 987 - 1003
[34] On a nonlinear stochastic wave equation in the plane: Existence and uniqueness of the solution
Millet, A
Morien, PL
ANNALS OF APPLIED PROBABILITY, 2001, 11 (03) : 922 - 951
[35] On the decay of solutions of the wave equation with logarithmic damping
Su, Xiao
Zhang, Chenxia
Zhang, Hongwei
APPLICABLE ANALYSIS, 2025,
[36] Nonlinear wave equation with damping: Periodic forcing and non-resonant solutions to the Kuznetsov equation
Celik, Aday
Kyed, Mads
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2018, 98 (03): : 412 - 430
[37] Approximate Controllability of a Stochastic Wave Equation
Jong Uhn Kim
Applied Mathematics and Optimization, 2004, 49 : 81 - 98
[38] Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping
P. Jameson Graber
Journal of Evolution Equations, 2012, 12 : 141 - 164
[39] Approximate controllability of a stochastic wave equation
Kim, JU
APPLIED MATHEMATICS AND OPTIMIZATION, 2004, 49 (01) : 81 - 98
[40] Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping
Graber, P. Jameson
JOURNAL OF EVOLUTION EQUATIONS, 2012, 12 (01) : 141 - 164

← 1 2 3 4 5 →