Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 22, pp. 1-27.

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

Authors: Jiangwei Zhang (National Univ. of Defense Technology, Changsha, China)
         Zhe Xie (Sinoma Wind Power Blade Co. Ltd, Beijing, China)
         Yongqin Xie (Changsha Univ. of Science and Technology, Changsha, China)

Abstract: 
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.