数学

时间依赖记忆型经典反应扩散方程的拉回吸引子

  • 李玉娜 ,
  • 汪璇
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  • 西北师范大学 数学与统计学院, 兰州 730070
汪 璇, 女, 教授, 研究方向为非线性微分方程和无穷维动力系统. E-mail: wangxuan@nwnu.edu.cn

收稿日期: 2023-11-20

  网络出版日期: 2025-01-20

基金资助

国家自然科学基金(11961059, 12061062)

版权

华东师范大学学报期刊社, 2025, 版权所有,未经授权,不得转载、摘编本刊文章,不得使用本刊的版式设计。

Pullback attractors for the classical reaction-diffusion equation with time-dependent memory kernel

  • Yuna LI ,
  • Xuan WANG
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  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received date: 2023-11-20

  Online published: 2025-01-20

Copyright

, 2025, Copyright reserved © 2025.

摘要

关于具有时间依赖记忆核的经典反应扩散方程, 当非线性项满足次临界增长, 外力项$ g(x, t)\in $$ L^{2}_{{\mathrm{loc}}}(\mathbb{R};L^{2}(\varOmega)) $时, 在时间依赖空间$ L^{2}(\varOmega)\times L_{\mu_{t}}^2(\mathbb{R}_{+}; H_{0}^1(\varOmega)) $中讨论了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证明了解的适定性和正则性, 进而证明了时间依赖拉回吸引子的存在性.

本文引用格式

李玉娜 , 汪璇 . 时间依赖记忆型经典反应扩散方程的拉回吸引子[J]. 华东师范大学学报(自然科学版), 2025 , 2025(1) : 28 -45 . DOI: 10.3969/j.issn.1000-5641.2025.01.003

Abstract

This paper presents a discussion on the long-time dynamical behavior of solutions for the classical reaction-diffusion equation with time-dependent memory kernel when nonlinear term adheres to subcritical growth and the external force term $g(x,t) $ belongs to the space $ L^{2}_{{\mathrm{loc}}}(\mathbb{R};L^{2}(\varOmega)) $ in the time-dependent space $ L^2(\varOmega)\times L_{\mu_{t}}^2(\mathbb{R}_{+}; H_{0}^1(\varOmega)) $. Within the new theorical framework, the well-posedness and the regularity of the solution, as well as the existence of the time-dependent pullback attractors are established. This is achieved by applying the delicate integral estimation method and decomposition techniques.

参考文献

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