Regularity of random attractors for non-autonomous stochastic strong damped wave equations driven by linear memory and additive noise

Abstract

In this paper, the study identified existence regularity of a random attractor for the stochastic dynamical system generated by non-autonomous strongly damping wave equation with linear memory and additive noise defined on Rn. First, to prove the existence of the pullback absorbing set and the pullback asymptotic compactness of the cocycle in a certain parameter region by using tail estimates and the decomposition technique of solutions. Then it proved the existence and uniqueness of a random attractor.