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Pullback measure attractors for stochastic p-Laplacian parabolic equations on thin domains

Part of: Partial differential equations Infinite-dimensional dissipative dynamical systems Stochastic analysis

Published online by Cambridge University Press:  05 August 2025

Zhe Pu
Zhe Pu*
Affiliation:
Department of Mathematics and Great Bay Institute for Advanced Study, Great Bay University, Dongguan 523000, P.R. China School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P.R. China (zhepuws@gbu.edu.cn)
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Abstract

We investigate the pullback measure attractors for non-autonomous stochastic p-Laplacian equations driven by nonlinear noise on thin domains. The concept of complete orbits for such systems is presented to establish the structures of pullback measure attractors. We first present some essential uniform estimates, as well as the existence and uniqueness of pullback measure attractors. A novel technical proof method is shown to overcome the difficulty of the estimates of the solutions in $W^{1,p}$ on thin domains. Then, we prove the upper semicontinuity of these measure attractors as the $(n + 1)$-dimensional thin domains collapse onto the lower n-dimensional space.

Keywords

measure attractorsnonlinear noisestochastic p-Laplacian equationthin domains

MSC classification

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 37L55: Infinite-dimensional random dynamical systems; stochastic equations 37L30: Attractors and their dimensions, Lyapunov exponents 60H15: Stochastic partial differential equations

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 28
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

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