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arXiv · 1309.1211

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

Andrew Krause·Bixiang Wang
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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.

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Andrew Krause, Bixiang Wang. 2013-09-05. Pullback Attractors of Non-autonomous Stochastic Degenerate Parabolic Equations on Unbounded Domains. https://doi.org/10.1016/j.jmaa.2014.03.037

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