Jiangwei Zhang, Zhe Xie, Yongqin Xie
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
DOI: 10.58997/ejde.2023.22
Show me the PDF file (471 KB), TEX file for this article.
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Jiangwei Zhang College of Science National University of Defense Technology Changsha 410073, China email: zjwmath@163.com |
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Zhe Xie Research and Development Center Sinoma Wind Power Blade Co. Ltd, Beijing 100192, China email: xiezhe890917@126.com |
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Yongqin Xie School of Mathematics and Statistics Changsha University of Science and Technology Changsha, 410114, China email: xieyqmath@126.com |
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