# American Institute of Mathematical Sciences

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

## Compact uniform attractors for dissipative non-autonomous lattice dynamical systems

 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.
Citation: Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087
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