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Research Article | Open Access

Finite fractal dimension of pullback attractors for a nonclassical diffusion equation

Xiaolei Dong1, Yuming Qin2,3( )
College of Information Science and Technology, Donghua University, Shanghai 201620, China
Department of Mathematics, Donghua University, Shanghai 201620, China
Institute for Nonlinear Science, Donghua University, Shanghai 201620, China
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Abstract

In this paper, we investigate the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in H 0 1 ( Ω ). First, we prove the existence of pullback attractors for a nonclassical diffusion equation with arbitrary polynomial growth condition by applying the operator decomposition method. Then, by the fractal dimension theorem of pullback attractors given by [6], we prove the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in H 0 1 ( Ω ).

Keywords

nonclassical diffusion equationsfinite fractal dimensionpullback attractors
CLC number: 35B40, 35B41, 35K57, 37F10

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8064-8079
DOI: 10.3934/math.2022449

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Cite this article:
Dong X, Qin Y. Finite fractal dimension of pullback attractors for a nonclassical diffusion equation. AIMS Mathematics, 2022, 7(5): 8064-8079. https://doi.org/10.3934/math.2022449

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Received: 08 January 2022
Revised: 11 February 2022
Accepted: 17 February 2022
Published: 15 May 2022
©2022 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)