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Existence and regularity of time-dependent pullback attractors for the non-autonomous nonclassical diffusion equations

Part of: Parabolic equations and systems Partial differential equations

Published online by Cambridge University Press:  18 November 2021

Yuming Qin  and
Bin Yang
Yuming Qin
Affiliation:
Department of Mathematics, Institute for Nonlinear Science, Donghua University, Shanghai 201620, People's Republic of China [email protected]
Bin Yang
Affiliation:
College of Information Science and Technology, Donghua University, Shanghai 201620, People's Republic of China [email protected]
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Abstract

In this paper, we prove the existence and regularity of pullback attractors for non-autonomous nonclassical diffusion equations with nonlocal diffusion when the nonlinear term satisfies critical exponential growth and the external force term $h \in L_{l o c}^{2}(\mathbb {R} ; H^{-1}(\Omega )).$ Under some appropriate assumptions, we establish the existence and uniqueness of the weak solution in the time-dependent space $\mathcal {H}_{t}(\Omega )$ and the existence and regularity of the pullback attractors.

Keywords

Non-autonomous nonclassical diffusion equationstime-dependent pullback attractorsregularity

MSC classification

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35B41: Attractors 35B65: Smoothness and regularity of solutions 35K57: Reaction-diffusion equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 6 , December 2022 , pp. 1533 - 1550
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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