Compact kernel sections for dissipative non-autonomous Zakharov equation on infinite lattices

Shengfan Zhou; Jinwu Huang; Xiaoying Han

doi:10.3934/cpaa.2010.9.193

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2010, Volume 9, Issue 1: 193-210. Doi: 10.3934/cpaa.2010.9.193

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Compact kernel sections for dissipative non-autonomous Zakharov equation on infinite lattices

1.
Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234
2.
221 Parker Hall, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849

Received: January 2009

Revised: May 2009

Published online: October 2009

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Abstract

In this paper, we first prove the existence of compact kernel sections for dissipative non-autonomous Zakharov lattice dynamical system, then we obtain an upper bound of fractal dimension of the compact kernel sections, and finally we establish an upper semicontinuity of the compact kernel sections.

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

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Compact kernel sections for dissipative non-autonomous Zakharov equation on infinite lattices

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