Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped sine-Gordon equation on unbounded domains

摘要

In this paper we study the asymptotic behavior of solutions of the non-autonomous stochastic strongly damped sine-Gordon equation driven by multiplicative noise defined on an unbounded domain. First we introduce a continuous cocycle for the equation and establish the pullback asymptotic compactness of solutions. Second we consider the existence and upper semicontinuity of random attractors for the equation. (C) 2017 Elsevier Ltd. All rights reserved.