Pullback Attractors of Non-autonomous Stochastic Degenerate Parabolic Equations on Unbounded Domains
- Resource Type
- Working Paper
- Authors
- Krause, Andrew; Wang, Bixiang
- Source
- Subject
- Mathematics - Analysis of PDEs
35B40 (Primary) 35B41, 37L30 (Secondary)
- Language
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-autonomous 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.