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Random Exponential Attractor for Stochastic Non-autonomous Suspension Bridge Equation with Linear multiplicative white noise

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Journal of Mathematical Research with Applications 2024年第1期44卷 81-112页

作者： Ling XU Runjie LIU Xue BAI College of Mathematics and Statistics Northwest Normal University

In this paper, we mainly consider the long-time behavior of stochastic non-autonomous suspension bridge equation by linear multiplicative white noise with small coefficient. First step,the well-posedness for the cocycle associated with the considered system is established. Second step, the existence of random attractor for the system is investigated. Third step, the upper semicontinuity of random attractor is also provided when the coefficient of random term approaches zero. Fourth step, we prove the regularity of random attractor in a higher regular space by the“iteration” method. Finally, we give the existence of a random exponential attractor for the considered system, which implies the finiteness of fractal dimension of random attractor.

关键词： stochastic non-autonomous suspension bridge equation multiplicative white noise random attractor fractal dimension random exponential attractor

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Random Attractors for Partly Dissipative Stochastic Lattice Dynamical Systems with multiplicative white noises

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Acta Mathematicae Applicatae Sinica 2015年第2期31卷 567-576页

作者： An-hui GU Sheng-fan ZHOU Qing-fei JIN School of Mathematics and Statistics Southwest University Department of Mathematics Zhejiang Normal University Shanghai Mingzhu Middle School

The present paper is devoted to the existence of the random attractor for partly dissipative stochastic lattice dynamical systems with multiplicative white noises.

关键词： random attractor multiplicative white noise partly dissipative stochastic lattice dynamical systems

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A Family of the Random Attractors for a Class of Generalized Kirchhoff-Type Equations

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Journal of Applied Mathematics and Physics 2021年第11期9卷 2966-2978页

作者： Guoguang Lin Lujiao Yang Department of Mathematics Yunnan University Kunming China

In this paper, we studied the existence of a family of the random attractor for a class of generalized Kirchhoff-type equations with a strong dissipation term. Firstly, according to Ornstein-Uhlenbeck process, we transformed the equation into a stochastic equation with random variables and multiplicative white noise. Secondly, we proved the existence of a bounded random absorbing set. Finally, by using the isomorphic mapping method and the compact embedding theorem, we get the stochastic dynamical system with a family of random attractors.

关键词： Stochastic Kirchhoff Equation A Family of the Random Attractors multiplicative white noise Ornstein-Uhlenbeck Process

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