Pullback measure attractors for non-autonomous stochastic reaction-diffusion equations on thin domains

This paper is concerned with pullback measure attractors of the non-autonomous stochastic reaction-diffusion equations defined in thin domains. We first prove the existence and uniqueness of pullback measure attractors for the inhomogeneous Markov process associated with the stochastic equations. We...

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Bibliographic Details
Published in:Journal of Differential Equations 2024-07, Vol.397, p.232-261
Main Authors: Li, Dingshi, Wang, Bixiang
Format: Article
Language:English
Subjects:
Complete solution
Inhomogeneous Markov process
Pullback measure attractor
Stochastic equation
Thin domain
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Summary:This paper is concerned with pullback measure attractors of the non-autonomous stochastic reaction-diffusion equations defined in thin domains. We first prove the existence and uniqueness of pullback measure attractors for the inhomogeneous Markov process associated with the stochastic equations. We also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback measure attractors. Then we establish the upper semi-continuity of these attractors as a family of thin domains collapses into a lower-dimensional domain.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2024.03.010