EXISTENCE AND UPPER SEMICONTINUITY OF RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC STRONGLY DAMPED WAVE EQUATION WITH MULTIPLICATIVE NOISE

In this paper we study the asymptotic behavior of solutions of the non-autonomous stochastic strongly damped wave equation driven by multiplicative noise defined on unbounded domains. We first introduce a continuous cocycle for the equation. Then we consider the existence of a tempered pullback random attractor for the cocycle. Finally we establish the upper semicontinuity of random attractors as the coefficient of the white noise term tends to zero.