Limiting dynamics for stochastic wave equations
نویسندگان
چکیده
In this paper, relations between the asymptotic behavior for a stochastic wave equation and a heat equation are considered. By introducing almost surely D–α-contracting property for random dynamical systems, we obtain a global random attractor of the stochastic wave equation νutt + ut − uν + f (uν) = √ νẆ endowed with Dirichlet boundary condition for any 0 < ν 1. The upper semicontinuity of this global random attractor and the global attractor of the heat equation zt − z+ 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. © 2007 Elsevier Inc. All rights reserved.
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