Taiwanese Journal of Mathematics

RANDOM ATTRACTOR FOR FRACTIONAL GINZBURG-LANDAU EQUATION WITH MULTIPLICATIVE NOISE

Hong Lu and Shujuan Lü

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Abstract

In this paper, we consider the asymptotic behavior of solutions to the stochastic fractional complex Ginzburg-Landau equation with multiplicative noise in one spatial dimensions. We first transfer stochastic fractional Ginzburg-Landau equation into random equation which solutions generate a random dynamical system. Then, we consider the existence of a random attractor for the random dynamical system. At last we estimate the Hausdorff dimension of the random attractor by using linearization and Lyapunov exponents.

Article information

Source
Taiwanese J. Math., Volume 18, Number 2 (2014), 435-450.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706395

Digital Object Identifier
doi:10.11650/tjm.18.2014.3053

Mathematical Reviews number (MathSciNet)
MR3188512

Zentralblatt MATH identifier
1357.37086

Subjects
Primary: 37L55: Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15] 60H15: Stochastic partial differential equations [See also 35R60] 35Q99: None of the above, but in this section

Keywords
stochastic fractional Ginzburg-Landau equation asymptotic compactness random attractor Hausdorff dimension

Citation

Lu, Hong; Lü, Shujuan. RANDOM ATTRACTOR FOR FRACTIONAL GINZBURG-LANDAU EQUATION WITH MULTIPLICATIVE NOISE. Taiwanese J. Math. 18 (2014), no. 2, 435--450. doi:10.11650/tjm.18.2014.3053. https://projecteuclid.org/euclid.twjm/1499706395


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