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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 217608, 6 pages
http://dx.doi.org/10.1155/2015/217608
Research Article

The Existence of Exponential Attractor for Discrete Ginzburg-Landau Equation

1Institute of Geotechnical Engineering, Southeast University, Nanjing, Jiangsu 210096, China
2State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China
3Department of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Received 17 May 2015; Accepted 13 September 2015

Academic Editor: Chris Goodrich

Copyright © 2015 Guangyin Du et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the following discrete systems of the complex Ginzburg-Landau equation: . Under some conditions on the parameters , and , we prove the existence of exponential attractor for the semigroup associated with these discrete systems.