Dynamics of the non-autonomous stochastic p-Laplacian parabolic problems on unbounded thin domains

This paper focuses on the dynamics of the non-autonomous stochastic p-Laplacian parabolic problems defined on unbounded thin domains. We first show that the tails of solutions of the equation are uniformly small outside a bounded domain, which is utilized to overcome the non-compactness of Sobolev e...

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Bibliographic Details
Published in:Journal of mathematical physics 2023-08, Vol.64 (8)
Main Authors: Pu, Zhe, Li, Dingshi
Format: Article
Language:English
Subjects:
Physics
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Summary:This paper focuses on the dynamics of the non-autonomous stochastic p-Laplacian parabolic problems defined on unbounded thin domains. We first show that the tails of solutions of the equation are uniformly small outside a bounded domain, which is utilized to overcome the non-compactness of Sobolev embeddings on unbounded domains. We then prove the existence and uniqueness of random attractors for the equations defined on (n + 1)-dimensional unbounded thin domains and further establish the upper semi-continuity of attractors as the thin domains collapse onto the space Rn.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0154808