Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains

By Andrew L. Krause, Bixiang Wang. 2013

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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.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/6d3d4c86c080a90a3d187258b69b959905fe7c30