Dynamics of non-autonomous fractional stochastic Ginzburg-Landau equations with multiplicative noise

Yun Lan; Ji Shu

doi:10.3934/cpaa.2019109

Article Contents

2019, Volume 18, Issue 5: 2409-2431. Doi: 10.3934/cpaa.2019109

This issue Previous Article Refined regularity for the blow-up set at non characteristic points for the vector-valued semilinear wave equation Next Article Existence and decay property of ground state solutions for Hamiltonian elliptic system

Dynamics of non-autonomous fractional stochastic Ginzburg-Landau equations with multiplicative noise

Yun Lan^1, and
Ji Shu^2, ,

1.
School of Mathematical Science, Sichuan Normal University, Chengdu, Sichuan 610068, China
2.
School of Mathematical Science and V.C. & V.R. Key Lab, Sichuan Normal University, Chengdu, Sichuan 610068, China

^* Corresponding author
^* Corresponding author

Received: March 31, 2018

Revised: June 30, 2018

Published: March 2019

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Abstract

This paper is concerned with the asymptotic behavior of solutions for non-autonomous stochastic fractional complex Ginzburg-Landau equations driven by multiplicative noise with $ \alpha\in(0, 1) $. We first apply the Galerkin method and compactness argument to prove the existence and uniqueness of weak solutions, which is slightly different from the deterministic fractional case with $ \alpha\in(\frac{1}{2}, 1) $ and the real fractional case with $ \alpha\in(0, 1) $. Consequently, we establish the existence and uniqueness of tempered pullback random attractors for the equations in a bounded domain. At last, we obtain the upper semicontinuity of random attractors when the intensity of noise approaches zero.

Keywords:

Non-autonomous stochastic fractional Ginzburg-Landau equation,
random dynamical system,
random attractor,
multiplicative noise,
upper semicontinuity.

Mathematics Subject Classification: Primary: 37L55, 60H15; Secondary: 35Q56.

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