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December  2007, 6(4): 1087-1111. doi: 10.3934/cpaa.2007.6.1087

Compact uniform attractors for dissipative non-autonomous lattice dynamical systems

Xinyuan Liao 1, , Caidi Zhao 2, and  Shengfan Zhou 3,

1. 

College of Science, Nanhua University, Hunan 421001, Christmas Island
2. 

College of Mathematics and Information Science, Wenzhou University, Zhejiang, 325035, China
3. 

Department of Mathematics, Shanghai University, Shanghai, 200436

Received  September 2006 Revised  March 2007 Published  September 2007

This paper discusses the long time behavior of solutions for dissipative non-autonomous lattice dynamical systems. We first prove some sufficient and necessary conditions for the existence of a compact uniform attractor for the family of processes defined on a Hilbert space of infinite sequences, and then give an upper bound of the Kolmogorov $\varepsilon$-entropy for the uniform attractor. As an application, we consider the dissipative non-autonomous lattice Zakharov equations.
Keywords: lattice Zakharov equations, Kolmogorov $\varepsilon$-entropy, Lattice dynamical systems, non-autonomous., uniform attractor.
Mathematics Subject Classification: Primary: 35B40, 35Q55; Secondary: 37L5.
Citation: Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure and Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087
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