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June  2008, 21(2): 643-663. doi: 10.3934/dcds.2008.21.643

Compact uniform attractors for dissipative lattice dynamical systems with delays

Caidi Zhao 1, and  Shengfan Zhou 2,

1. 

College of Mathematics and Information Science, Wenzhou University, Zhejiang, 325035
2. 

Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234

Received  January 2007 Revised  October 2007 Published  March 2008

In this paper, we consider the long time behavior of solutions for dissipative lattice dynamical systems with delays. We first prove a sufficient and necessary condition for the existence of a compact uniform attractor for the family of processes corresponding to the lattice dynamical systems with delays. Then we apply this result to prove the existence of a compact uniform attractor for the process associated to the retarded lattice Zakharov equations. As a consequence, some results for the non-delay lattice dynamical systems are deduced as particular cases.
Keywords: Lattice dynamical systems; Uniform attractor; Delay systems; Kolmogorov $\varepsilon$-entropy..
Mathematics Subject Classification: 35B40; 37L50; 35Q5.
Citation: Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative lattice dynamical systems with delays. Discrete and Continuous Dynamical Systems, 2008, 21 (2) : 643-663. doi: 10.3934/dcds.2008.21.643
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