Limiting dynamics for stochastic wave equations

  title={Limiting dynamics for stochastic wave equations},
  author={Yan Chun Lv and Wei Wang},
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… CONTINUE READING