Random attractors and averaging for non-autonomous stochastic wave equations with nonlinear damping

This paper is devoted to the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with nonlinear damping and multiplicative white noise defined on an unbounded domain. By showing the pullback asymptotic compactness of the cocycle in a certain parameter region, we prove the existence of a random attractor when the intensity of noise is sufficiently small. For the stochastic wave equation with rapidly oscillating external force we prove that the Hausdorff distance between the random attractor AϵAϵ of the original equation and the random attractor A0A0 of the averaged equation is in the order of O(ϵ)O(ϵ).