Compact uniform attractors for dissipative non-autonomous lattice dynamical systems

Xinyuan Liao; Caidi Zhao; Shengfan Zhou

doi:10.3934/cpaa.2007.6.1087

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2007, Volume 6, Issue 4: 1087-1111. Doi: 10.3934/cpaa.2007.6.1087

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Compact uniform attractors for dissipative non-autonomous lattice dynamical systems

1.
College of Science, Nanhua University, Hunan 421001
2.
College of Mathematics and Information Science, Wenzhou University, Zhejiang, 325035
3.
Department of Mathematics, Shanghai University, Shanghai, 200436

Received: August 31, 2006

Revised: February 28, 2007

Published: November 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35Q55; Secondary: 37L50.

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