American Institute of Mathematical Sciences

Advanced
May  2008, 9(3&4, May): 763-785. doi: 10.3934/dcdsb.2008.9.763

Kernel sections for processes and nonautonomous lattice systems

Xiao-Qiang Zhao 1, and  Shengfan Zhou 2,

1. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NF A1C 5S7
2. 

Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234

Received  October 2006 Revised  January 2007 Published  February 2008

In this paper, we first establish a set of sufficient and necessaryconditions for the existence of globally attractive kernel sectionsfor processes defined on a general Banach space and a weighted spaceℓ$_\rho ^p$ of infinite sequences ($p\geq 1)$, respectively.Then we obtain an upper bound of the Kolmogorov$\varepsilon$-entropy of kernel sections for processes on theHilbert space ℓ$_\rho ^2 $. As applications, we investigatecompact kernel sections for first order, partly dissipative, andsecond order nonautonomous lattice systems on weighted spacescontaining bounded sequences.
Keywords: Kernel sections, lattice systems, pullback asymptotic null., pullback $\omega $-limit compactness, Kolmogorov's $\varepsilon $-entropy.
Mathematics Subject Classification: 35B40, 34A35, 37L3.
Citation: Xiao-Qiang Zhao, Shengfan Zhou. Kernel sections for processes and nonautonomous lattice systems. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 763-785. doi: 10.3934/dcdsb.2008.9.763
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