Uniform random attractors for a non-autonomous stochastic strongly damped wave equation on RN

The aim of this paper is to investigate the existence of uniform random attractor for a non-autonomous stochastic strongly damped wave equation driven by multiplicative noise defined on R-N (1 <= N <= 3). First, we prove the equation can generate a non-autonomous random dynamical system (NRDS), which is continuous in both phase space H-1 (R-N) x L-2 (R-N) and symbol space. Then, we derive the uniform estimates of solutions for the equation and obtain a uniform random absorbing set with respect to the symbols. Finally, we get the uniformly asymptotic compactness of the NRDS by using the method of tail estimates and obtain the existence of a uniform random attractor for the dynamical system. Furthermore, we can also obtain that the uniform random attractor with respect to the deterministic non-autonomous symbols belonging to hull space coincides with the uniform random attractor with respect to initial time belonging to R.