Abstract
Abstract
In this paper, existence of invariant measure is mainly investigated for a fractional stochastic delay reaction–diffusion equation defined on unbounded domains. We first establish the mean-square uniform smallness of the tails of the solutions in order to overcome the non-compactness of standard Sobolev embeddings on unbounded domains. We then show the weak compactness of a family of probability distributions of the solutions by combining the Ascoli–Arzelà theorem, the uniform tail-estimates as well as the technique of dyadic division.
Funder
Natural Science Foundation of Shandong Province
National Natural Science Foundation of China
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
13 articles.
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