THE EXISTENCE OF RANDOM ATTRACTORS FOR PLATE EQUATIONS WITH MEMORY AND ADDITIVE WHITE NOISE

We investigate the asymptotic behavior of a class of non-autonomous stochastic FitzHugh–Nagumo systems driven by additive white noise on unbounded thin domains. For this aim, we first show the existence and uniqueness of random attractors for the considered equations and their limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse into a lower-dimensional unbounded domain.

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Fractal Dimension for the Nonautonomous Stochastic Fifth-Order Swift–Hohenberg Equation

Complexity ◽

10.1155/2020/8864585 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Yanfeng Guo ◽

Chunxiao Guo ◽

Yongping Xi

Keyword(s):

Fractal Dimension ◽

White Noise ◽

Bounded Domain ◽

Unbounded Domain ◽

Random Attractor ◽

Additive White Noise ◽

Random Attractors ◽

Fifth Order

Some dynamics behaviors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with additive white noise are considered. The existence of pullback random attractors for the nonautonomous stochastic fifth-order Swift–Hohenberg equation with some properties is mainly investigated on the bounded domain and unbounded domain, through the Ornstein–Uhlenbeck transformation and tail-term estimates. Furthermore, on the basis of some conditions, the finiteness of fractal dimension of random attractor is proved.

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Wong–Zakai approximations of second-order stochastic lattice systems driven by additive white noise

Stochastics and Dynamics ◽

10.1142/s0219493721500507 ◽

2021 ◽

pp. 2150050

Author(s):

Yiju Chen ◽

Chunxiao Guo ◽

Xiaohu Wang

Keyword(s):

White Noise ◽

Additive Noise ◽

Upper Semicontinuity ◽

Second Order ◽

Pullback Attractors ◽

Lattice Systems ◽

Additive White Noise ◽

Random Attractors ◽

Approximate System

In this paper, we study the Wong–Zakai approximations of a class of second-order stochastic lattice systems with additive noise. We first prove the existence of tempered pullback attractors for lattice systems driven by an approximation of the white noise. Then, we establish the upper semicontinuity of random attractors for the approximate system as the size of approximation approaches zero.

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Random Attractors for Stochastic Retarded Lattice Dynamical Systems

Abstract and Applied Analysis ◽

10.1155/2012/409282 ◽

2012 ◽

Vol 2012 ◽

pp. 1-27 ◽

Cited By ~ 4

Author(s):

Xiaoquan Ding ◽

Jifa Jiang

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

White Noise ◽

Random Attractor ◽

Additive White Noise ◽

Lattice Dynamical System ◽

Random Attractors ◽

Lattice Dynamical Systems ◽

Bounded Sets

This paper is devoted to a stochastic retarded lattice dynamical system with additive white noise. We extend the method of tail estimates to stochastic retarded lattice dynamical systems and prove the existence of a compact global random attractor within the set of tempered random bounded sets.

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Stochastic Euler–Bernoulli beam driven by additive white noise: Global random attractors and global dynamics

Nonlinear Analysis ◽

10.1016/j.na.2019.03.007 ◽

2019 ◽

Vol 185 ◽

pp. 216-246 ◽

Cited By ~ 1

Author(s):

Huatao Chen ◽

Juan Luis García Guirao ◽

Dengqing Cao ◽

Jingfei Jiang ◽

Xiaoming Fan

Keyword(s):

White Noise ◽

Global Dynamics ◽

Bernoulli Beam ◽

Additive White Noise ◽

Random Attractors ◽

Euler Bernoulli Beam

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Random attractors for stochastic delay wave equations on $ \mathbb{R}^n $ with linear memory and nonlinear damping

Discrete and Continuous Dynamical Systems - Series S ◽

10.3934/dcdss.2021141 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Jingyu Wang ◽

Yejuan Wang ◽

Lin Yang ◽

Tomás Caraballo

Keyword(s):

Wave Equation ◽

White Noise ◽

Unbounded Domain ◽

Existence And Uniqueness ◽

Wave Equations ◽

Nonlinear Damping ◽

Random Attractor ◽

Stochastic Delay ◽

Additive White Noise ◽

Random Attractors

<p style='text-indent:20px;'>A non-autonomous stochastic delay wave equation with linear memory and nonlinear damping driven by additive white noise is considered on the unbounded domain <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula>. We establish the existence and uniqueness of a random attractor <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{A} $\end{document}</tex-math></inline-formula> that is compact in <inline-formula><tex-math id="M3">\begin{document}$ C{([-h, 0];H^1(\mathbb{R}^n))}\times C{([-h, 0];L^2(\mathbb{R}^n))}\times L_\mu^2(\mathbb{R}^+;H^1(\mathbb{R}^n)) $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M4">\begin{document}$ 1\leqslant n \leqslant 3 $\end{document}</tex-math></inline-formula>.</p>

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Wong–Zakai approximations and limiting dynamics of stochastic Ginzburg–Landau equations

Stochastics and Dynamics ◽

10.1142/s021949372250006x ◽

2021 ◽

Author(s):

Ji Shu ◽

Dandan Ma ◽

Xin Huang ◽

Jian Zhang

Keyword(s):

White Noise ◽

Landau Equation ◽

Upper Semicontinuity ◽

Approximate Equation ◽

Ginzburg Landau ◽

Random System ◽

Additive White Noise ◽

Random Attractors ◽

Ginzburg Landau Equations ◽

Weaker Conditions

This paper deals with the Wong–Zakai approximations and random attractors for stochastic Ginzburg–Landau equations with a white noise. We first prove the existence of a pullback random attractor for the approximate equation under much weaker conditions than the original stochastic equation. In addition, when the stochastic Ginzburg–Landau equation is driven by an additive white noise, we establish the convergence of solutions of Wong–Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation tends to zero.

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