Fractal dimension of random attractors for non-autonomous fractional stochastic Ginzburg–Landau equations with multiplicative noise. Issue 2 (3rd April 2019)

• Record Type: Journal Article
• Authors: Lan, Yun; Shu, Ji
• Is Part Of: Dynamical systems. Volume 34:Issue 2(2019)
• Page Start: 274
• Page End: 300
• Publication Date: 2019-04-03
• Subjects: Non-autonomous stochastic fractional Ginzburg–Landau equation -- random dynamical system -- random attractor -- multiplicative noise -- fractal dimension; 37L55 -- 60H15 -- 35Q56; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2018.1523368
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: This paper deals with the asymptotic behaviour of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by multiplicative noise withα ∈ ( 0, 1 ) . We first present some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Then we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equations inL 2 ( R n ) . At last, we prove the finiteness of fractal dimension of random attractors.