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Research Article | Open Access

Time-dependent asymptotic behavior of the solution for evolution equation with linear memory

Tingting Liu1, Tasneem Mustafa Hussain Sharfi2, Qiaozhen Ma1( )
College of Mathematics and Statistics, Northwest Normal University, Gansu, 730070, Lanzhou, China
Faculty of Mathematical science, University of Khartoum, Sudan
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Abstract

In this article, by using the operator decomposition technique, we discuss the existence of a time-dependent global attractor for a nonlinear evolution equation with linear memory within the theory of time-dependent space. Furthermore, the regularity and asymptotic structure of the time-dependent attractor are proved, which means that the time-dependent attractor of the evolution equation converges to the attractor of the limit wave equation when the coefficient ε ( t ) → 0 as t → ∞.

Keywords

linear memorytime-dependent global attractorregularityasymptotic structure
CLC number: 35B40, 35B41, 37L30

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16208-16227
DOI: 10.3934/math.2023829

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Cite this article:
Liu T, Sharfi TMH, Ma Q. Time-dependent asymptotic behavior of the solution for evolution equation with linear memory. AIMS Mathematics, 2023, 8(7): 16208-16227. https://doi.org/10.3934/math.2023829

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Received: 09 February 2023
Revised: 06 April 2023
Accepted: 17 April 2023
Published: 15 July 2023
©2023 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)