scholarly journals Upper semicontinuity of random attractors for the stochastic non-autonomous suspension bridge equation with memory

2017 ◽  
Vol 22 (11) ◽  
pp. 1-21
Author(s):  
Ling Xu ◽  
◽  
Jianhua Huang ◽  
Qiaozhen Ma ◽  
Keyword(s):  
Upper Semicontinuity ◽  
Suspension Bridge ◽  
Random Attractors ◽  
With Memory

Dynamics of stochastic FitzHugh–Nagumo systems with additive noise on unbounded thin domains

2019 ◽  
Vol 20 (03) ◽  
pp. 2050018
Author(s):  
Lin Shi ◽  
Dingshi Li ◽  
Xiliang Li ◽  
Xiaohu Wang
Keyword(s):  
Asymptotic Behavior ◽  
White Noise ◽  
Unbounded Domain ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Upper Semicontinuity ◽  
Thin Domains ◽  
Additive White Noise ◽  
Random Attractors ◽  
Lower Dimensional

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.

scholarly journals Upper Semicontinuity of Random Attractors for Nonautonomous Stochastic Reversible Selkov System with Multiplicative Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Chunxiao Guo ◽  
Yanfeng Guo ◽  
Xiaohan Li
Keyword(s):  
Multiplicative Noise ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Main Difficulty ◽  
Asymptotic Compactness ◽  
Random Attractors

In this paper, the existence of random attractors for nonautonomous stochastic reversible Selkov system with multiplicative noise has been proved through Ornstein-Uhlenbeck transformation. Furthermore, the upper semicontinuity of random attractors is discussed when the intensity of noise approaches zero. The main difficulty is to prove the asymptotic compactness for establishing the existence of tempered pullback random attractor.

scholarly journals Asymptotic behavior for non-autonomous stochastic plate equation on unbounded domains

2019 ◽  
Vol 17 (1) ◽  
pp. 1281-1302 ◽  
Author(s):  
Xiaobin Yao ◽  
Xilan Liu
Keyword(s):  
Asymptotic Behavior ◽  
Additive Noise ◽  
Upper Semicontinuity ◽  
Unbounded Domains ◽  
Asymptotic Behavior Of Solutions ◽  
Plate Equation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Random Attractors

Abstract We study the asymptotic behavior of solutions to the non-autonomous stochastic plate equation driven by additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence and upper semicontinuity of random attractors.

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

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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