RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC WAVE EQUATIONS WITH MULTIPLICATIVE NOISE

This paper is concerned with the asymptotic behavior of solutions of the damped non-autonomous stochastic wave equations driven by multiplicative white noise. We prove the existence of pullback random attractors in H-1(R-n) x L-2(R-n) when the intensity of noise is sufficiently small. We demonstrate that these random attractors are periodic in time if so are the deterministic non-autonomous external terms. We also establish the upper semicontinuity of random attractors when the intensity of noise approaches zero. In addition, we prove the measurability of random attractors even if the underlying probability space is not complete.