The asymptotic behavior of the stochastic Ginzburg–Landau equation with additive noise

Wang, Guolian; Guo, Boling; Li, Yangrong

doi:10.1016/j.amc.2007.09.029

Cited by 26 publications

(12 citation statements)

References 7 publications

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“…Recently, the concept of random attractors, which is in fact compact invariant set, was introduced to stochastic dynamical systems from the theory of attractors for deterministic equations in [8][9][10]. The existence of such random attractors for the Ginzburg-Landau equation perturbed by additive white noise and multiplicative white noise on bounded domains has been investigated, respectively, in [11,12].…”

Section: Introductionmentioning

confidence: 99%

Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

Deng

Zhang

2014

Abstract and Applied Analysis

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We prove the existence of a pullback attractor in L 2 (R ) for the stochastic Ginzburg-Landau equation with additive noise on the entire n-dimensional space R . 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 unique D-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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Section: Introductionmentioning

confidence: 99%

Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

Deng

Zhang

2014

Abstract and Applied Analysis

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“…To handle the deterministic non-autonomous force and random force in a unified framework, Wang in [30] defined the concept of pullback random attractor for non-autonomous random dynamical system. There is a enormous number of publications on pullback random attractors, which, for instance, can be found in [4,5,10,11,12,13,14,18,19,30,31,32,35] for autonomous stochastic systems and in [31,33,34] for non-autonomous stochastic systems.…”

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confidence: 99%

Asymptotic behavior of stochastic complex Ginzburg-Landau equations with deterministic non-autonomous forcing on thin domains

Li¹,

Wang²

2019

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, we investigate the asymptotic behavior for nonautonomous stochastic complex Ginzburg-Landau equations with multiplicative noise on thin domains. For this aim, we first show that the existence and uniqueness of random attractors for the considered equations and the limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse onto an interval.

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“…where s ∈ R, λ, κ, γ > 0, Ω is a bounded smooth domain in R n with n = 1, 2 and the unknown u is a complex-valued function. If the coefficients α(•) and β(•) are constants, then a global attractor was obtained in [31] for f ≡ 0 and a random attractor was obtained in [36] if f is replaced by an additive noise.…”

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confidence: 99%

Longtime robustness and semi-uniform compactness of a pullback attractor via nonautonomous PDE

Li¹,

She²,

Yin³

2018

Discrete &Amp; Continuous Dynamical Systems - B

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This paper is concerned with the robustness of a pullback attractor as the time tends to infinity. A pullback attractor is called forward (resp. backward) compact if the union over the future (resp. the past) is pre-compact. We prove that the forward (resp. backward) compactness is a necessary and sufficient condition such that a pullback attractor is upper semi-continuous to a compact set at positive (resp. negative) infinity, and also obtain the minimal limit-set. We further prove the lower semi-continuity of the pullback attractor and get the maximal limit-set at infinity. Some criteria for such robustness are established when the evolution process is forward or backward omegalimit compact. Those theoretical criteria are applied to prove semi-uniform compactness and robustness at infinity in pullback dynamics for a Ginzburg-Landau equation with variable coefficients and a forward or backward tempered nonlinearity.

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The asymptotic behavior of the stochastic Ginzburg–Landau equation with additive noise

Cited by 26 publications

References 7 publications

Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

Asymptotic behavior of stochastic complex Ginzburg-Landau equations with deterministic non-autonomous forcing on thin domains

Longtime robustness and semi-uniform compactness of a pullback attractor via nonautonomous PDE

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