Electron. J. Differential Equations, Vol. 2024 (2024), No. 22, pp. 1-27.

Asymptotic behavior of solutions to nonclassical diffusion equations with degenerate memory and a time-dependent perturbed parameter

Jiangwei Zhang, Zhe Xie, Yongqin Xie

This article concerns the asymptotic behavior of solutions for a class of nonclassical diffusion equation with time-dependent perturbation coefficient and degenerate memory. We prove the existence and uniqueness of time-dependent global attractors in the family of time-dependent product spaces, by applying the operator decomposition technique and the contractive function method. Then we study the asymptotic structure of time-dependent global attractors as \(t\to \infty\). It is worth noting that the memory kernel function satisfies general assumption, and the nonlinearity \(f\) satisfies a polynomial growth of arbitrary order.

Submitted November 9, 2023. Published March 12, 2024.
Math Subject Classifications: 35K57, 35B40, 35B41.
Key Words: Nonclassical diffusion equation; time-dependent global attractor; polynomial growth; contractive function; asymptotic structure
DOI: 10.58997/ejde.2023.22

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Jiangwei Zhang
College of Science
National University of Defense Technology
Changsha 410073, China
email: zjwmath@163.com
Zhe Xie
Research and Development Center
Sinoma Wind Power Blade Co. Ltd, Beijing
100192, China
email: xiezhe890917@126.com
Yongqin Xie
School of Mathematics and Statistics
Changsha University of Science and Technology
Changsha, 410114, China
email: xieyqmath@126.com

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