ATTRACTORS FOR THE NONCLASSICAL DIFFUSION EQUATION WITH TIME-DEPENDENT MEMORY KERNEL AND CRITICAL NONLINEARITY

Xuan Wang; Haiyan Yuan; Xiaoling Han; Chenghua Gao

doi:10.11948/20230130

2025 Volume 15 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(5): 2474-2507

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Xuan Wang, Haiyan Yuan, Xiaoling Han, Chenghua Gao. ATTRACTORS FOR THE NONCLASSICAL DIFFUSION EQUATION WITH TIME-DEPENDENT MEMORY KERNEL AND CRITICAL NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2474-2507. doi: 10.11948/20230130

Citation:

Xuan Wang, Haiyan Yuan, Xiaoling Han, Chenghua Gao. ATTRACTORS FOR THE NONCLASSICAL DIFFUSION EQUATION WITH TIME-DEPENDENT MEMORY KERNEL AND CRITICAL NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2474-2507. doi: 10.11948/20230130

ATTRACTORS FOR THE NONCLASSICAL DIFFUSION EQUATION WITH TIME-DEPENDENT MEMORY KERNEL AND CRITICAL NONLINEARITY

1.
College of Mathematics and Statistics, Northwest Normal University, Anning East Road, 730070 Lanzhou, China
2.
Zhongshan Jianbin Vacational and Technical School, Wendongnan Street, 528415 Zhongshan, China

Author Bio: Email: 1872412053@qq.com(H. Yuan); Email: hanxiaoling9@163.com(X. Han); Email: gaochenghua@nwnu.edu.cn(C. Gao)
Corresponding author: Email: wangxuan@nwnu.edu.cn(X. Wang)
Fund Project: The authors were supported by National Natural Science Foundation of China (12161079, 12461039, 11961059, 12061062)

Abstract

Abstract

In this paper, we consider the long-time dynamics of solutions for the nonclassical diffusion equation with time-dependent memory kernel when nonlinear term adheres to critical growth, where the time-dependent memory kernel is used to describe the aging process of viscoelastic conductive medium. Under the new theory framework, we first establish the well-posedness and regularity of the solutions, and then we prove the existence and regularity of the time-dependent global attractors in the time-dependent space $H_0^1(\Omega)\times L_{\mu_t}^2(\mathbb R^+; H_0^1(\Omega))$ by use of the delicate integral estimation method and decomposition technique.
- Nonclassical diffusion equation /
- time-dependent memory kernel /
- time-dependent global attractors /
- regularity
MSC: 35B40, 35B41

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References

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