# American Institute of Mathematical Sciences

January  2010, 9(1): 193-210. doi: 10.3934/cpaa.2010.9.193

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

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

Received  January 2009 Revised  May 2009 Published  October 2009

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.
Citation: Shengfan Zhou, Jinwu Huang, Xiaoying Han. Compact kernel sections for dissipative non-autonomous Zakharov equation on infinite lattices. Communications on Pure & Applied Analysis, 2010, 9 (1) : 193-210. doi: 10.3934/cpaa.2010.9.193
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