On the Stochastic Wave Equation with Nonlinear Damping

被引：0
作者：
Jong Uhn Kim
机构：
[1] Virginia Tech,Department of Mathematics
来源：
Applied Mathematics and Optimization | 2008年 / 58卷
关键词：
Wave equation; Nonlinear damping; Initial boundary value problem; Brownian motion; Invariant measure;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：29 / 67
页数：38
相关论文
共 25 条
  • [1] Arrietta J.(1992)A damped hyperbolic equation with critical exponents Commun. Partial Differ. Equ. 17 841-866
  • [2] Carvalho A.N.(2002)The stochastic nonlinear damped wave equation Appl. Math. Optim. 46 125-141
  • [3] Hale J.(2005)On nonlinear wave equations with degenerate damping and source terms Trans. Am. Math. Soc. 357 2571-2611
  • [4] Barbu V.(2002)Stochastic wave equations with polynomial nonlinearity Ann. Appl. Probab. 12 361-381
  • [5] Da Prato G.(2002)On the attractors for a semilinear wave equation with critical exponent and nonlinear boundary dissipation Commum. Partial Differ. Equ. 27 1901-1951
  • [6] Barbu V.(1997)Random attractors J. Dyn. Differ. Equ. 9 307-341
  • [7] Lasiecka I.(1995)Global attractors for damped wave equations with supercritical exponent J. Differ. Equ. 116 431-447
  • [8] Rammaha M.(2004)Periodic and invariant measures for stochastic wave equations Electron. J. Differ. Equ. 5 30-1703
  • [9] Chow P.L.(2005)Invariant measures for the stochastic von Karman plate equation SIAM J. Math. Anal. 36 1689-113
  • [10] Chueshov I.(1937)La théorie générale de la mesure dans son application à l’étude des systémes de la Mécanique non linéaire Ann. Math. 38 65-96
123