吉林大学学报(理学版) ›› 2025, Vol. 63 ›› Issue (2): 297-0306.

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具有记忆项的双曲型Cahn-Hilliard方程时间依赖吸引子及其正则性

曹宇宇, 姜金平, 刘丹, 王碧琪   

  1. 延安大学 数学与计算机科学学院, 陕西 延安 716000
  • 收稿日期:2024-04-09 出版日期:2025-03-26 发布日期:2025-03-26
  • 通讯作者: 姜金平 E-mail:jpjiang@yau.edu.cn

Time-Dependent Attractor and Its Regularity of Hyperbolic Cahn-Hilliard Equation with Memory Term

CAO Yuyu, JIANG Jinping, LIU Dan, WANG Biqi   

  1. College of Mathematics and Computer Science, Yan’an University, Yan’an 716000, Shaanxi Province, China
  • Received:2024-04-09 Online:2025-03-26 Published:2025-03-26

摘要: 考虑具有线性记忆项的双曲型Cahn-Hilliard方程解的长时间动力学行为, 在时间依赖速度传播的作用下, 利用渐近先验估计、 算子分解方法以及修正的拉回吸引子理论, 证明该方程在时间依赖空间中吸引子的存在性及正则性.

关键词: 双曲型Cahn-Hilliard方程, 线性记忆项, 时间依赖吸引子, 算子分解, 正则性

Abstract: We considered the long-term dynamic behavior of solutions to hyperbolic Cahn-Hilliard equations with linear memory terms. Under the action of time-dependent velocity propagation, the existence and regularity of the attractor in  time-dependent  space of the equation were proved by using asymptotic prior  equation, operator  decomposition method and modified pullback attractor theory.

Key words: hyperbolic Cahn-Hilliard equation, linear memory term, time-dependent attractor, operator decomposition, regularity

中图分类号: 

  • O175.29