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time-dependent pullback attractors

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Existence and regularity of time-dependent pullback attractors for the non-autonomous nonclassical diffusion equations
Part of
- Partial differential equations
- Parabolic equations and systems
Yuming Qin, Bin Yang
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 6 / December 2022

Published online by Cambridge University Press:

18 November 2021, pp. 1533-1550

Print publication:

December 2022
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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.