华东师范大学学报（自然科学版） ›› 2025, Vol. 2025 ›› Issue (1): 28-45.doi: 10.3969/j.issn.1000-5641.2025.01.003

• 数学 • 上一篇    下一篇

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*()   

  1. 西北师范大学 数学与统计学院, 兰州　730070
  • 收稿日期:2023-11-20 出版日期:2025-01-25 发布日期:2025-01-20
  • 通讯作者: 汪璇 E-mail:wangxuan@nwnu.edu.cn
  • 基金资助:
    国家自然科学基金(11961059, 12061062)

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

Yuna LI, Xuan WANG*()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou　730070, China
  • Received:2023-11-20 Online:2025-01-25 Published:2025-01-20
  • Contact: Xuan WANG E-mail:wangxuan@nwnu.edu.cn

RichHTML

28

PDF

293

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.

关键词: 经典反应扩散方程, 时间依赖记忆核, 适定性, 时间依赖拉回吸引子, 存在性

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.

Key words: classical reaction-diffusion equation, time-dependent memory kernel, well-posedness, time-dependent pullback attractors, existence

中图分类号: