Global attractors for the discrete Klein-Gordon-Schrödinger type equations

Chunqiu Li, Cheng Hsiung Hsu, Jian Jhong Lin, Caidi Zhao

研究成果: 雜誌貢獻期刊論文同行評審

10 引文 斯高帕斯(Scopus)

摘要

The purpose of this work is to investigate the asymptotic behaviours of solutions for the discrete Klein-Gordon-Schrödinger type equations in one-dimensional lattice. We first establish the global existence and uniqueness of solutions for the corresponding Cauchy problem. According to the solution's estimate, it is shown that the semi-group generated by the solution is continuous and possesses an absorbing set. Using truncation technique, we show that there exists a global attractor for the semi-group. Finally, we extend the criteria of Zhou et al. [S. Zhou, C. Zhao, and Y. Wang, Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems, Discrete Contin. Dyn. Syst. A 21 (2008), pp. 1259-1277.] for finite fractal dimension of a family of compact subsets in a Hilbert space to obtain an upper bound of fractal dimension for the global attractor.

原文???core.languages.en_GB???
頁(從 - 到)1404-1426
頁數23
期刊Journal of Difference Equations and Applications
20
發行號10
DOIs
出版狀態已出版 - 10月 2014

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