Attractors for a class of perturbed nonclassical diffusion equations with memory

Jianbo Yuan; Shixuan Zhang; Yongqin Xie; Jiangwei Zhang

doi:10.3934/dcdsb.2021261

Article Contents

2022, Volume 27, Issue 9: 4995-5007. Doi: 10.3934/dcdsb.2021261

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Attractors for a class of perturbed nonclassical diffusion equations with memory

1.
School of Traffic and Transportation Engineering, Changsha University of Science and Technology, Changsha, Changsha Hunan 410114, China
2.
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Changsha Hunan 410114, China
3.
College of Science, National University of Defense Technology, Changsha Hunan 410073, China

^* Corresponding author: Yongqin Xie
^* Corresponding author: Yongqin Xie

Received: May 31, 2021

Revised: August 31, 2021

Early access: November 2021

Published: September 2022

The work was partly supported by NSFS grants 51578080, 11101053, 71471020, Postgraduate scientific research innovation project of Hunan Province (CX20210751)

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Abstract

In this paper, using a new operator decomposition method (or framework), we establish the existence, regularity and upper semi-continuity of global attractors for a perturbed nonclassical diffusion equation with fading memory. It is worth noting that we get the same conclusion in [7,14] as the perturbed parameters $ \nu = 0 $, but the nonlinearity $ f $ satisfies arbitrary polynomial growth condition rather than critical exponential growth condition.

Correction: “College of Arts and Sciences” has been changed to "College of Science"; “Postgraduate scientific research innovation project of Hunan Province (CX20210751)” has been added to Fund Project. We apologize for any inconvenience this may cause.

Keywords:

The perturbed nonclassical diffusion equation,
arbitrary polynomial growth,
global attractor,
upper semi-continuity.

Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 35K57.

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