Limiting dynamics for stochastic wave equations
Date
2008
Authors
Lv, Y.
Wang, W.
Editors
Advisors
Journal Title
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Volume Title
Type:
Journal article
Citation
Journal of Differential Equations, 2008; 244(1):1-23
Statement of Responsibility
Yan Lv and Wei Wang
Conference Name
Abstract
In this paper, relations between the asymptotic behavior for a stochastic wave equation and a heat equation are considered. By introducing almost surely –α-contracting property for random dynamical systems, we obtain a global random attractor of the stochastic wave equation endowed with Dirichlet boundary condition for any 0<ν1. The upper semicontinuity of this global random attractor and the global attractor of the heat equation zt−Δz+f(z)=0 with Dirichlet boundary condition as ν goes to zero is investigated. Furthermore we show the stationary solutions of the stochastic wave equation converge in probability to some stationary solution of the heat equation