2021
DOI: 10.1017/prm.2021.65
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Existence and regularity of time-dependent pullback attractors for the non-autonomous nonclassical diffusion equations

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 … Show more

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Cited by 4 publications
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“…About the related works concerning attractors of Timoshenko or porous-elastic systems, we refer to [7][8][9]22,23] for the case of two linear or nonlinear frictional damping.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…About the related works concerning attractors of Timoshenko or porous-elastic systems, we refer to [7][8][9]22,23] for the case of two linear or nonlinear frictional damping.…”
Section: Introductionmentioning
confidence: 99%
“…There have been a lot of studies on the decay rate estimation of solutions to Timoshenko or porous‐elastic systems with memory (see, e.g., [1–24] and references therein), while there are just a few studies on global attractors of such systems.…”
Section: Introductionmentioning
confidence: 99%