Dynamics of the non-autonomous stochastic p-Laplace equation driven by multiplicative noise

We investigate the asymptotic behavior of solutions of the p-Laplace equation driven simultaneously by non-autonomous deterministic forcing and multiplicative white noise on Rn. We show the tails of solutions of the equation are uniformly small outside a bounded domain, which is used to derive asymptotic compactness of solution operators in L2(Rn) by overcoming the non-compactness of Sobolev embeddings on unbounded domains. We then prove existence and uniqueness of random attractors and further establish upper semicontinuity of attractors as the intensity of noise approaches zero.