分数阶非局部反应扩散方程的随机吸引子及不变测度

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 949-962.

分数阶非局部反应扩散方程的随机吸引子及不变测度

杨裔瑶(), 姜金平^*(), 马楠楠()

延安大学数学与计算机科学学院陕西延安 716000

收稿日期:2024-10-18 修回日期:2025-10-21 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 姜金平 E-mail:2407497163@qq.com;E-mail:yadxjjp@163.com;E-mail:826585775@qq.com
作者简介:杨裔瑶, E-mail:2407497163@qq.com;
马楠楠, E-mail:826585775@qq.com
基金资助:
陕西数理基础科学研究项目(23JSY050)

Stochastic Attractors and Invariant Measures for Fractional Nonlocal Reaction-Diffusion Equations

Yiyao Yang(), Jinping Jiang^*(), Nannan Ma()

School of Mathematics and Computer Science, Yan'an University, Shaanxi Yanan 716000

Received:2024-10-18 Revised:2025-10-21 Online:2026-06-26 Published:2026-06-16
Contact: Jinping Jiang E-mail:2407497163@qq.com;E-mail:yadxjjp@163.com;E-mail:826585775@qq.com
Supported by:
Shaanxi Mathematical Basic Science Research Program(23JSY050)

摘要/Abstract

摘要：

该文研究了一类由非线性色噪声驱动的分数阶非局部反应扩散方程的动力学行为. 首先, 通过 $\text{Galerkin}$ 方法给出带非线性色噪声的方程解的存在性. 其次, 在适当的 $\text{Hilbert}$ 空间中证明了该方程拉回随机吸引子的存在唯一性. 最后, 利用广义 $\text{Banach}$ 极限方法证明了该方程不变测度的存在性.

关键词: 分数阶非局部反应扩散方程, 随机吸引子, 不变测度, 色噪声.

Abstract:

This paper investigates the dynamical behavior of a class of fractional nonlocal reaction-diffusion equation driven by nonlinear colored noise. Firstly, the existence of solutions to the equations with nonlinear colored noise is given by the Galerkin method. Secondly, the existence of the pullback stochastic attractor for this equation is proved in an appropriate Hilbert space. Finally, the generalized Banach limit is used to prove the existence of invariant measures for this equation.

Key words: fractional nonlocal reaction-diffusion equation, random attractor, invariant measure, colored noise.

中图分类号:

O175.2

杨裔瑶, 姜金平, 马楠楠. 分数阶非局部反应扩散方程的随机吸引子及不变测度[J]. 数学物理学报, 2026, 46(3): 949-962.

Yiyao Yang, Jinping Jiang, Nannan Ma. Stochastic Attractors and Invariant Measures for Fractional Nonlocal Reaction-Diffusion Equations[J]. Acta mathematica scientia,Series A, 2026, 46(3): 949-962.

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