AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (249.9 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
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
Show Author Information

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

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8064-8079
DOI: 10.3934/math.2022449

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
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

29

Views

0

Downloads

1

Crossref

1

Web of Science

1

Scopus
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)