Taylor and Francis Ltd.;Abingdon: Taylor & Francis
摘要:
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. 出版者： Abingdon: Taylor & Francis 出版日期： 2014-10-03 出處： Journal of difference equations and applications, 2014-10, Vol.20 (10), p.1404-1426 版權： 2014 Taylor & Francis 2014 版權： Copyright Taylor & Francis Ltd. 2014 識別號： ISSN: 1023-6198 識別號： EISSN: 1563-5120 識別號： DOI: 10.1080/10236198.2014.933821
