Pullback Attractors of Non-autonomous Stochastic Degenerate Parabolic Equations on Unbounded Domains

TL;DR

This paper investigates the existence and properties of pullback attractors for stochastic p-Laplace equations on unbounded domains, demonstrating their existence, uniqueness, and periodicity under certain conditions.

Contribution

It establishes the asymptotic compactness and existence of non-autonomous random attractors for stochastic degenerate parabolic equations on unbounded domains, addressing non-compactness challenges.

Findings

Existence and uniqueness of pullback attractors.

Pathwise periodicity under time-periodic forcing.

Overcoming non-compact Sobolev embedding issues.

Abstract

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.