Pullback random attractors of stochastic strongly damped wave equations with variable delays on unbounded domains

Abstract

In this paper, we consider the asymptotic behavior of solutions to stochastic strongly damped wave equations with variable delays on unbounded domains, which is driven by both additive noise and deterministic non-autonomous forcing. We first establish a continuous cocycle for the equations. Then we prove asymptotic compactness of the cocycle by tail-estimates and a decomposition technique of solutions. Finally, we obtain the existence of a tempered pullback random attractor.

Keywords

• strongly damped wave equation
• variable delays
• random attractor
• asymptotical compactness
• tail-estimates