加权空间中非自治离散修正 Swift-Hohenberg 方程的统计解

数学物理学报 ›› 2025, Vol. 45 ›› Issue (5): 1586-1601.

加权空间中非自治离散修正 Swift-Hohenberg 方程的统计解

何曼露^*(),黎定仕

西南交通大学数学学院成都 610031

收稿日期:2024-11-05 修回日期:2025-02-15 出版日期:2025-10-26 发布日期:2025-10-14
通讯作者: * 何曼露,E-mail:actams@wipm.ac.cn; actams@apm.ac.cn
基金资助:
国家自然科学基金(11971394);国家自然科学基金(12371178);中央引导地方基金(2023ZYD0002)

Statistical Solutions for the Nonautonomous Discrete Modified Swift-Hohenberg Equation in Weighted Spaces

Manlu He^*(),Dingshi Li

School of Mathematics, Southwest Jiaotong University, Chengdu 610031

Received:2024-11-05 Revised:2025-02-15 Online:2025-10-26 Published:2025-10-14
Supported by:
NSFC(11971394);NSFC(12371178);Fundamental Research Funds for the Central Universities(2023ZYD0002)

摘要/Abstract

摘要：

该文研究了加权空间中非自治离散修正 Swift-Hohenberg 方程的统计解. 首先证明了该方程在加权空间中拉回吸引子的存在性. 然后证明了解算子生成的过程存在一族不变 Borel 概率测度. 最后证明了该族不变测度是该系统的统计解.

关键词: 统计解, 加权空间, 离散修正 Swift-Hohenberg 方程

Abstract:

This paper studies the statistical solutions for the nonautonomous modified Swift-Hohenberg equation in weighted spaces. The authors first show the existence of pullback attractors of the process generated by this equation. Then the paper further establishes the existence of a unique family of invariant Borel probability measures carried by the pullback attractors, and finally prove that the family of invariant Borel probability measures is a statistical solution for this equation.

Key words: statistical solution, weighted space, discrete modified Swift-Hohenberg equation

中图分类号:

O193

何曼露, 黎定仕. 加权空间中非自治离散修正 Swift-Hohenberg 方程的统计解[J]. 数学物理学报, 2025, 45(5): 1586-1601.

Manlu He, Dingshi Li. Statistical Solutions for the Nonautonomous Discrete Modified Swift-Hohenberg Equation in Weighted Spaces[J]. Acta mathematica scientia,Series A, 2025, 45(5): 1586-1601.

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