Random Attractors for Delay Parabolic Equations with Additive Noise and Deterministic Nonautonomous Forcing

2015 ◽  
Vol 14 (2) ◽  
pp. 1018-1047 ◽  
Author(s):  
Xiaohu Wang ◽  
Kening Lu ◽  
Bixiang Wang
Keyword(s):  
Parabolic Equations ◽  
Additive Noise ◽  
Random Attractors

scholarly journals Random attractors for stochastic parabolic equations with additive noise in weighted spaces

2018 ◽  
Vol 17 (3) ◽  
pp. 729-749 ◽  
Author(s):  
Xiaojun Li ◽  
◽  
Xiliang Li ◽  
Kening Lu ◽  
◽  
...  
Keyword(s):  
Parabolic Equations ◽  
Additive Noise ◽  
Weighted Spaces ◽  
Random Attractors

Inverse problems for stochastic parabolic equations with additive noise

2020 ◽  
Vol 29 (1) ◽  
pp. 93-108
Author(s):  
Ganghua Yuan
Keyword(s):  
Inverse Problems ◽  
Parabolic Equations ◽  
Additive Noise ◽  
Stability Result ◽  
Main Tool ◽  
Conditional Stability ◽  
Final Time ◽  
History Of ◽  
Global Carleman Estimate ◽  
Stochastic Parabolic Equation

Abstract In this paper, we study two inverse problems for stochastic parabolic equations with additive noise. One is to determinate the history of a stochastic heat process and the random heat source simultaneously by the observation at the final time 𝑇. For this inverse problem, we obtain a conditional stability result. The other one is an inverse source problem to determine two kinds of sources simultaneously by the observation at the final time and on the lateral boundary. The main tool for solving the inverse problems is a new global Carleman estimate for the stochastic parabolic equation.

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.

scholarly journals Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qiuying Lu ◽  
Guifeng Deng ◽  
Weipeng Zhang
Keyword(s):  
Additive Noise ◽  
Dimensional Space ◽  
Landau Equation ◽  
Unbounded Domains ◽  
Random Dynamical System ◽  
Pullback Attractor ◽  
Ginzburg Landau ◽  
Uniform Estimates ◽  
Ginzburg Landau Equation ◽  
Random Attractors

We prove the existence of a pullback attractor inL2(ℝn)for the stochastic Ginzburg-Landau equation with additive noise on the entiren-dimensional spaceℝn. We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a uniqueD-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.

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