Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems

Shengfan Zhou; Caidi Zhao; Yejuan Wang

doi:10.3934/dcds.2008.21.1259

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2008, Volume 21, Issue 4: 1259-1277. Doi: 10.3934/dcds.2008.21.1259

This issue Previous Article Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations Next Article Preface

Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems

1.
Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234
2.
Institute of Nonlinear Analysis, Department of Mathematics and Information Science, Wenzhou University, Zhejiang, Wenzhou 325035
3.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000

Received: June 2007

Revised: April 2008

Published: October 2008

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we first establish a criteria for finite fractal dimensionality of a family of compact subsets of a Hilbert space, and apply it to obtain an upper bound of fractal dimension of compact kernel sections to first order non-autonomous lattice systems. Then we consider the upper semicontinuity of kernel sections of general first order non-autonomous lattice systems and give an application.

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Mathematics Subject Classification: 35B40, 37L50, 35Q55.

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