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Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains [PDF]
Abstract and Applied Analysis, 2013 This paper is devoted to a stochastic retarded reaction-diffusion equation on all d-dimensional space with additive white noise. We first show that the stochastic retarded reaction-diffusion equation generates a random dynamical system by transforming ...
Xiaoquan Ding, Jifa Jiang
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Advances in Difference Equations, 2019 This paper is concerned with the random exponential attractor for second order non-autonomous stochastic lattice system with multiplicative white noise and unbounded nonlinearity.
Haijuan Su, Shengfan Zhou, Luyao Wu
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Existence of random attractors and the upper semicontinuity for small random perturbations of 2D Navier-Stokes equations with linear damping [PDF]
Open Mathematics, 2021 The incompressible 2D stochastic Navier-Stokes equations with linear damping are considered in this paper. Based on some new calculation estimates, we obtain the existence of random attractor and the upper semicontinuity of the random attractors as ε→0 ...
Li Haiyan, Wang Bo
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Random attractor for a damped sine-Gordon equation with white noise [PDF]
, 2004 Xiaoming Fan
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Evolution Equations and Control Theory, 2020 A pullback random attractor is called forward controllable if its time-component is semi-continuous to a compact set in the future, and the minimum among all such compact limit-sets is called a forward controller.
Shuang Yang, Yangrong Li
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Random attractor for stochastic Hindmarsh-Rose equations with multiplicative noise [PDF]
Discrete & Continuous Dynamical Systems - B, 2019 The longtime and global pullback dynamics of stochastic Hindmarsh-Rose equations with multiplicative noise on a three-dimensional bounded domain in neurodynamics is investigated in this work.
Chi Phan
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Probabilistic continuity of a pullback random attractor in time-sample
Discrete & Continuous Dynamical Systems - B, 2020 Given a time-sample dependent attractor of a random dynamical system, we study its lower semi-continuity in probability along the time axis, and the criteria are established by using the local-sample asymptotically compactness for a triple-continuous ...
Shulin Wang, Yangrong Li
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Random attractor for second-order stochastic delay lattice sine-Gordon equation
Boundary Value Problems, 2021 In this paper, we prove the existence of random D $\mathcal{D}$ -attractor for the second-order stochastic delay sine-Gordon equation on infinite lattice with certain dissipative conditions, and then establish the upper bound of Kolmogorov ε-entropy for ...
Xintao Li, Lianbing She, Zhenpei Shan
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, 2020 In this paper, we study the backward compactness of random attractors, which describes the compactness of the union \begin{document}$ \cup_{s\leq\tau}\mathcal A(s,\omega) $\end{document} of random attractor sections over past times, \begin{document ...
Fuzhi Li, Dongmei Xu, Jiali Yu
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Dynamics of the stochastic wave equations with degenerate memory effects on bounded domain [PDF]
Surveys in Mathematics and its Applications, 2022 In this work, we consider the behavior of long-time dynamics of a random dynamical system generated wave equations with degenerate memory and additive noise, on bounded domain U, with Dirichlet boundary condition, and nonlinear term f(u) with critical ...
Abdelmajid A. D. +3 more
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