EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON ℝN

doi:10.1007/s10473-025-0418-x

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (4): 1567-1596.doi: 10.1007/s10473-025-0418-x

EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON ℝ^N

Huijuan ZHU¹, Xiaojun LI^1,*, Yanjiao LI²

1. School of Mathematics, Hohai University, Nanjing 210098, China;
2. School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

收稿日期:2024-01-17 出版日期:2025-10-10 发布日期:2025-10-10

EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON ℝ^N

Huijuan ZHU¹, Xiaojun LI^1,*, Yanjiao LI²

1. School of Mathematics, Hohai University, Nanjing 210098, China;
2. School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Received:2024-01-17 Online:2025-10-10 Published:2025-10-10
Contact: ^*Xiaojun LI, E-mail: lixjun05@hhu.edu.cn
About author:Huijuan ZHU, E-mail: zhuhuijuan2022@hhu.edu.cn; Yanjiao LI, E-mail: yanjiaoli2013@163.com
Supported by:
NSFC (12271141), and Zhu's research was supported by the Fundamental Research Funds for the Central Universities (B240205026), and the Postgraduate Research and Practice Innovation Program of Jiangsu Province (KYCX24_0821).

摘要/Abstract

摘要： In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined on $\mathbb{R}^n$. The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on $\mathbb{R}^n$.

关键词: random reaction-diffusion equation, continuous cocycle, pullback random attractor, fractal dimension, random exponential attractor

Abstract: In this paper, we consider the existence of pullback random exponential attractor for non-autonomous random reaction-diffusion equation driven by nonlinear colored noise defined on $\mathbb{R}^n$. The key steps of the proof are the tails estimate and to demonstrate the Lipschitz continuity and random squeezing property of the solution for the equation defined on $\mathbb{R}^n$.

Key words: random reaction-diffusion equation, continuous cocycle, pullback random attractor, fractal dimension, random exponential attractor

Huijuan ZHU, Xiaojun LI, Yanjiao LI. EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON ℝ^N[J]. 数学物理学报(英文版), 2025, 45(4): 1567-1596.

Huijuan ZHU, Xiaojun LI, Yanjiao LI. EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON ℝ^N[J]. Acta mathematica scientia,Series B, 2025, 45(4): 1567-1596.

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EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON ℝ^N

EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON ℝ^N

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