具有时间依赖记忆核的非经典扩散方程的吸引子

数学物理学报 ›› 2024, Vol. 44 ›› Issue (2): 429-452.

具有时间依赖记忆核的非经典扩散方程的吸引子

汪璇(),袁海燕^*()

西北师范大学数学与统计学院兰州 730070

收稿日期:2022-05-12 修回日期:2023-10-07 出版日期:2024-04-26 发布日期:2024-04-07
通讯作者: * 袁海燕,Email:yuanhy1872412053@126.com
作者简介:汪璇,Email:wangxuan@nwnu.edu.cn
基金资助:
国家自然科学基金(11961059);国家自然科学基金(12061062)

Attractors for the Nonclassical Diffusion Equation with Time-Dependent Memory Kernel

Wang Xuan(),Yuan Haiyan^*()

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070

Received:2022-05-12 Revised:2023-10-07 Online:2024-04-26 Published:2024-04-07
Supported by:
NSFC(11961059);NSFC(12061062)

摘要/Abstract

摘要：

该文在时间依赖空间 $H_{0}^1(\Omega)\times L_{\mu_{t}}^2(\mathbb R^+; H_{0}^1(\Omega))$ 中研究了具有时间依赖记忆核的非经典扩散方程解的长时间动力学行为. 在新的理论框架下, 利用积分估计方法以及分解技术得到了解的适定性, 进而证明了时间依赖全局吸引子的存在性与正则性.

关键词: 非经典扩散方程, 时间依赖记忆核, 适定性, 时间依赖全局吸引子, 吸引子的正则性

Abstract:

In this paper, we study the long-time dynamical behavior of solutions for the nonclassical diffusion equation with time-dependent memory kernel in the time-dependent space $H_{0}^1(\Omega)\times L_{\mu_{t}}^2(\mathbb R^+; H_{0}^1(\Omega))$. Under the new theorical framework, the well-posedness of the solution, the existence and the regularity of the time-dependent global attractors are proved by using the delicate integral estimation method and decomposition technique.

Key words: Nonclassical diffusion equation, Time-dependent memory kernel, Well-posedness, Time-dependent global attractors, Regularity of the attractors

中图分类号:

O175.29

汪璇, 袁海燕. 具有时间依赖记忆核的非经典扩散方程的吸引子[J]. 数学物理学报, 2024, 44(2): 429-452.

Wang Xuan, Yuan Haiyan. Attractors for the Nonclassical Diffusion Equation with Time-Dependent Memory Kernel[J]. Acta mathematica scientia,Series A, 2024, 44(2): 429-452.

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