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 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.

Limiting dynamics for stochastic FitzHugh–Nagumo equations on large domains

2019 ◽  
Vol 19 (05) ◽  
pp. 1950037 ◽  
Author(s):  
Yangrong Li ◽  
Fuzhi Li
Keyword(s):  
Bounded Domain ◽  
Unbounded Domain ◽  
Bounded Domains ◽  
Limit Set ◽  
Coupled Equations ◽  
Lower Semi ◽  
The Family ◽  
Random Attractors ◽  
Nagumo Equations ◽  
Theoretical Results

This paper is devoted to the convergence of bi-spatial random attractors as a family of bounded domains is extended to be unbounded. Some criteria in terms of expansion and restriction are provided to ensure that the unbounded-domain attractor is approximated by the family of bounded-domain attractors in both upper and lower semi-continuity senses. The theoretical results are applied to show that the stochastic FitzHugh–Nagumo coupled equations have an attractor in [Formula: see text]-times Lebesgue space irrespective of whether the domain is bounded or unbounded. Furthermore, we prove that the family of bounded-domain attractors continuously converges to the unbounded-domain attractor, and the latter can be constructed by the metric-limit set of all bounded-domain attractors.

scholarly journals Random Attractors of Stochastic Three-Component Reversible Gray-Scott System on Unbounded Domains

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Anhui Gu
Keyword(s):  
Dynamical System ◽  
A Priori Estimates ◽  
A Priori ◽  
Unbounded Domains ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Far Field ◽  
Asymptotic Compactness ◽  
Priori Estimates ◽  
Random Attractors

The existence of a pullback random attractor is established for a stochastic three-component reversible Gray-Scott system on unbounded domains. The Gray-Scott system is recast as a random dynamical system and asymptotic compactness which is illustrated by using uniform, a priori estimates for far-field values of solutions and a cutoff technique.

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 Random Attractors for the Stochastic Discrete Long Wave-Short Wave Resonance Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Jie Xin ◽  
Hong Lu
Keyword(s):  
Dynamical System ◽  
Short Wave ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Asymptotic Compactness ◽  
Infinite Lattice ◽  
Long Wave ◽  
Wave Resonance ◽  
Random Attractors

We prove the existence of the random attractor for the stochastic discrete long wave-short wave resonance equations in an infinite lattice. We prove the asymptotic compactness of the random dynamical system and obtain the random attractor.

scholarly journals Random attractors for semilinear reaction-diffusion equation with distribution derivatives and multiplicative noise on \(\mathbb{R}^{n}\)

2020 ◽  
Vol 4 (1) ◽  
pp. 126-141
Author(s):  
Fadlallah Mustafa Mosa ◽  
◽  
Abdelmajid Ali Dafallah ◽  
Eshag Mohamed Ahmed ◽  
Mohamed Y. A Bakhet ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Multiplicative Noise ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Random Attractors

scholarly journals Asymptotic behavior of supercritical wave equations driven by colored noise on unbounded domains

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Bixiang Wang
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Wave Equations ◽  
Colored Noise ◽  
Unbounded Domains ◽  
Strichartz Estimates ◽  
Well Posedness ◽  
Natural Energy ◽  
Random Attractors ◽  
Supercritical Nonlinearity

<p style='text-indent:20px;'>This paper deals with the asymptotic behavior of the non-autonomous random dynamical systems generated by the wave equations with supercritical nonlinearity driven by colored noise defined on <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M2">\begin{document}$ n\le 6 $\end{document}</tex-math></inline-formula>. Based on the uniform Strichartz estimates, we prove the well-posedness of the equation in the natural energy space and define a continuous cocycle associated with the solution operator. We also establish the existence and uniqueness of tempered random attractors of the equation by showing the uniform smallness of the tails of the solutions outside a bounded domain in order to overcome the non-compactness of Sobolev embeddings on unbounded domains.</p>

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.

Sign in / Sign up

Export Citation Format

Share Document