Stochastic dynamics of 2D fractional Ginzburg-Landau equationwith multiplicative noise

Shujuan Lü; Hong  Lu; Zhaosheng  Feng

doi:10.3934/dcdsb.2016.21.575

Article Contents

2016, Volume 21, Issue 2: 575-590. Doi: 10.3934/dcdsb.2016.21.575

This issue Previous Article On the analytic integrability of the Liénard analytic differential systems Next Article Monostable waves and spreading speed for a reaction-diffusion model with seasonal succession

Stochastic dynamics of 2D fractional Ginzburg-Landau equation with multiplicative noise

1.
School of Mathematics and Systems Science & LMIB, Beijing University of Aeronautics and Astronautics, Beijing, 100191
2.
School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191
3.
School of Mathematical and Statistical Sciences, University of Texas-Rio Grande Valley, Edinburg, TX 78539

Received: November 30, 2014

Revised: April 30, 2015

Published: February 2016

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Abstract

In this work, we analyze the stochastic fractional Ginzburg-Landau equation with multiplicative noise in two spatial dimensions with a particular interest in the asymptotic behavior of its solutions. To get started, we first transfer the stochastic fractional Ginzburg-Landau equation into a random equation whose solutions generate a random dynamical system. The existence of a random attractor for the resulting random dynamical system is explored, and the Hausdorff dimension of the random attractor is estimated.

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

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