scholarly journals Asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yiju Chen ◽  
Xiaohu Wang
Keyword(s):  
Asymptotic Behavior ◽  
Multiplicative Noise ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Discrete Laplacian ◽  
Lattice Systems ◽  
Random Attractors ◽  
Infinite Range Interactions ◽  
Infinite Range

<p style='text-indent:20px;'>In this paper, we study the asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise. The considered systems are driven by the fractional discrete Laplacian, which features the infinite-range interactions. We first prove the existence of pullback random attractor in <inline-formula><tex-math id="M1">\begin{document}$ \ell^2 $\end{document}</tex-math></inline-formula> for stochastic lattice systems. The upper semicontinuity of random attractors is also established when the intensity of noise approaches zero.</p>

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.

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 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.

scholarly journals Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Xiaoyao Jia ◽  
Xiaoquan Ding
Keyword(s):  
Additive Noise ◽  
Stochastic Equation ◽  
Stokes Equations ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Navier Stokes ◽  
Pullback Attractor ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Random Attractors

In this paper, the existence and the upper semicontinuity of a pullback attractor for stochastic retarded 2D-Navier-Stokes equation on a bounded domain are obtained. We first transform the stochastic equation into a random equation and then obtain the existence of a random attractor for random equation. Then conjugation relation between two random dynamical systems implies the existence of a random attractor for the stochastic equation. At last, we get the upper semicontinuity of random attractor.

Dynamic behavior of stochastic p-Laplacian-type lattice equations

2016 ◽  
Vol 17 (05) ◽  
pp. 1750040 ◽  
Author(s):  
Anhui Gu ◽  
Yangrong Li
Keyword(s):  
Dynamic Behavior ◽  
Multiplicative Noise ◽  
Finite Lattice ◽  
Unbounded Domains ◽  
Random Attractor ◽  
Infinite Lattice ◽  
Lower Semi ◽  
The Family ◽  
Random Attractors ◽  
Type Lattice

In this paper, we consider the dynamic behavior of stochastic [Formula: see text]-Laplacian-type lattice equations perturbed by a multiplicative noise. Under weaker dissipative conditions compared to the cases of stochastic [Formula: see text]-Laplacian-type equations in bounded and unbounded domains, we first obtain the existence of a unique random attractor. We also establish the approximation of the random attractors from finite lattice to infinite lattice, which indicates that the family of random attractors is upper and lower semi-continuous when the number of the lattice nodes tends to infinity.

scholarly journals Existence and Upper Semicontinuity of Attractors for Nonautonomous Stochastic Sine-Gordon Lattice Systems with Random Coupled Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Zhaojuan Wang ◽  
Shengfan Zhou
Keyword(s):  
White Noise ◽  
Weighted Space ◽  
Upper Semicontinuity ◽  
Lattice Systems ◽  
Random Attractors ◽  
Multiplicative White Noise

We study nonautonomous stochastic sine-Gordon lattice systems with random coupled coefficients and multiplicative white noise. We first consider the existence of random attractors in a weighted space for this system and then establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

scholarly journals Existence of Gibbs point processes with stable infinite range interaction

2020 ◽  
Vol 57 (3) ◽  
pp. 775-791
Author(s):  
David Dereudre ◽  
Thibaut Vasseur
Keyword(s):  
Point Processes ◽  
Existence Results ◽  
Pairwise Interaction ◽  
Range Interaction ◽  
Pairwise Interactions ◽  
Gibbs Point Processes ◽  
Infinite Range Interactions ◽  
Finite Configuration ◽  
Multi Body ◽  
Infinite Range

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

UNIFORM ATTRACTORS OF NONAUTONOMOUS DISCRETE REACTION–DIFFUSION SYSTEMS IN WEIGHTED SPACES

2008 ◽  
Vol 18 (03) ◽  
pp. 695-716 ◽  
Author(s):  
BIXIANG WANG
Keyword(s):  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Weighted Spaces ◽  
Lattice Systems ◽  
Limiting Behavior ◽  
Reaction Diffusion Systems ◽  
Nonautonomous Systems ◽  
Diffusion Systems ◽  
Uniform Attractors

We study the asymptotic behavior of nonautonomous discrete Reaction–Diffusion systems defined on multidimensional infinite lattices. We show that the nonautonomous systems possess uniform attractors which attract all solutions uniformly with respect to the translations of external terms when time goes to infinity. These attractors are compact subsets of weighted spaces, and contain all bounded solutions of the system. The upper semicontinuity of the uniform attractors is established when an infinite-dimensional reaction–diffusion system is approached by a family of finite-dimensional systems. We also examine the limiting behavior of lattice systems with almost periodic, rapidly oscillating external terms in weighted spaces. In this case, it is proved that the uniform global attractors of nonautonomous systems converge to the global attractor of an averaged autonomous system.

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