This thesis is concerned with the asymptotic behavior of solutions of stochastic $p$-Laplace equations driven by non-autonomous forcing on $mathbb{R}^n$. Two cases are studied, with additive and multiplicative noise respectively. Estimates on the tai
ls of solutions are used to overcome the non-compactness of Sobolev embeddings on unbounded domains, and prove asymptotic compactness of solution operators in $L^2(mathbb{R}^n)$. Using this result we prove the existence and uniqueness of random attractors in each case. Additionally, we show the upper semicontinuity of the attractor for the multiplicative noise case as the intensity of the noise approaches zero.
This paper is concerned with pullback attractors of the stochastic p-Laplace equation defined on the entire space R^n. We first establish the asymptotic compactness of the equation in L^2(R^n) and then prove the existence and uniqueness of non-autono
mous random attractors. This attractor is pathwise periodic if the non-autonomous deterministic forcing is time periodic. The difficulty of non-compactness of Sobolev embeddings on R^n is overcome by the uniform smallness of solutions outside a bounded domain.
