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Continuity Properties of Pullback and Pullback Exponential Attractors for Non-autonomous Plate with \(p-\)Laplacian

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Abstract

Our purpose is to study some continuity properties of pullback and pullback exponential attractors for the non-autonomous plate with \(p-\)Laplacian and nonlocal weak damping \(\text {g}_\epsilon (\Vert u_t\Vert )u_t\) under hinged boundary condition. Moreover, the existence of pullback attractors in the natural space energy with finite dimensionality is proved together with its upper semicontinuity and continuity with respect to the perturbed parameter \(\epsilon \in [0, 1]\). Finally, we prove that the related process has a pullback exponential attractor \({\mathscr {M}}^\epsilon _{exp}\) and is Hölder continuous on \(\epsilon \in [0, 1]\). In particular, the continuity on perturbation \(\epsilon \in [0,1]\) holds for global and exponential attractors when the non-autonomous dynamical system degenerates to an autonomous one.

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Acknowledgements

The author would like to thank the Editor in Chief Prof. Irena Lasiecka and the anonymous referees for their critical reviews and valuable comments which thoroughly improved the paper.

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  1. Université de Carthage, Ecole Nationale d’Ingénieurs de Bizerte, UR Systèmes Dynamiques et Applications, UR 17ES21, BP66, 7035, Bizerte, Tunisia

    Moncef Aouadi

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Aouadi, M. Continuity Properties of Pullback and Pullback Exponential Attractors for Non-autonomous Plate with \(p-\)Laplacian. Appl Math Optim 89, 10 (2024). https://doi.org/10.1007/s00245-023-10082-6

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