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Research Article | Open Access

Global attractors for a class of viscoelastic plate equations with past history

Quan Zhou1, Yang Liu1( ), Dong Yang2
College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
College of Creative Design, Chongqing City Vocational College, Chongqing 402160, China
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Abstract

This paper is concerned with a class of viscoelastic plate equations with past history. We first transform the original initial-boundary value problem into an equivalent one by means of the history space framework. Then we use the perturbed energy method to establish a stabilizability estimate. By employing the gradient property and quasi-stability of the dynamical system, we obtain the existence of a global attractor with finite fractal dimension.

Keywords

viscoelastic plate equationspast historyglobal attractorsgradient dynamical systemquasi-stability
CLC number: 35B41, 35L75, 37N15

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 24887-24907
DOI: 10.3934/math.20241212

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Cite this article:
Zhou Q, Liu Y, Yang D. Global attractors for a class of viscoelastic plate equations with past history. AIMS Mathematics, 2024, 9(9): 24887-24907. https://doi.org/10.3934/math.20241212

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Received: 27 June 2024
Revised: 06 August 2024
Accepted: 12 August 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)