格点时滞反应扩散方程的拉回吸引子与不变测度

数学物理学报 ›› 2025, Vol. 45 ›› Issue (4): 1128-1143.

格点时滞反应扩散方程的拉回吸引子与不变测度

倪思妍(),邹天芳(),赵才地^*()

温州大学数理学院浙江温州 325035

收稿日期:2024-09-11 修回日期:2025-01-10 出版日期:2025-08-26 发布日期:2025-08-01
通讯作者: *E-mail: zoutianfang0825@163.com
作者简介:E-mail: zhaocaidi@wzu.edu.cn;|1360245333@qq.com
基金资助:
国家自然科学基金(12371245);国家自然科学基金(11971356);浙江省自然科学基金重点项目(LZ24A010005)

Pullback Attractors and Invariant Measures for Retarded Lattice Reaction-Diffusion Equations

Ni Siyan(),Zou Tianfang(),Zhao Caidi^*()

Department of Mathematics, Wenzhou University, Zhejiang Wenzhou 325035

Received:2024-09-11 Revised:2025-01-10 Online:2025-08-26 Published:2025-08-01
Supported by:
NSFC(12371245);NSFC(11971356);Key project of Zhejiang Province's NSF(LZ24A010005)

摘要/Abstract

摘要：

该文研究无穷格点上时滞反应扩散方程拉回吸引子与不变测度的存在性. 作者首先证明格点时滞反应扩散方程初值问题解的全局适定性, 且解映射在相应相空间中生成一个连续过程, 然后证明该过程存在拉回吸引子, 并应用该拉回吸引子和广义 Banach 极限构造过程的不变 Borel 概率测度.

关键词: 格点时滞反应扩散方程, 拉回吸引子, 不变测度

Abstract:

In this article, the authors study the pullback attractor and invariant measures for retarded lattice reaction-diffusion equations. They first prove the global well-posedness of the addressed problem, and then show that the solution mappings generates a continuous process possessing a pullback attractor. Afterwards, they construct a family of invariant Borel probability measures for the process via the pullback attractor and the notion of generalized Banach limit.

Key words: retarded reaction-diffusion equations, pullback attractors, invariant measures

中图分类号:

O.175.8

倪思妍, 邹天芳, 赵才地. 格点时滞反应扩散方程的拉回吸引子与不变测度[J]. 数学物理学报, 2025, 45(4): 1128-1143.

Ni Siyan, Zou Tianfang, Zhao Caidi. Pullback Attractors and Invariant Measures for Retarded Lattice Reaction-Diffusion Equations[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1128-1143.

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