二阶时滞格子动力系统的全局吸引子

主要研究二阶时滞格子动力系统的全局吸引子的存在性.首先,通过定义向量v和正常数ε将原二阶时滞系统的吸引子存在性问题等价地转化为一阶二维时滞系统的吸引子存在性问题;然后证明此一阶二维时滞系统解的存在唯一性,接着对这个解进行先验估计,通过论证得到系统吸收集的存在性,另外利用对方程解的"尾部"在时间t足够大时所作的一致小估计讨论渐近紧性;最后证明系统全局吸引子的存在性.

Attractors for second-order retarded lattice dynamical systems

This paper concerns the existence of attractors for a second-order retarded lattice dynami-cal systems. By defining the number of ε and the vector of v, the original second-order retarded lat-tice dynamical systems is equivalent to a new first-order two-dimensional retarded systems. The uniqueness and existence is first proved for the solutions of the new lattice dynamical systems, and a priori estimate is obtained on the solutions. The existence of an absorbing set is then discussed for the systems. An estimate on tails of the solutions is derived when the time is large enough, which ensures the asymptotic compactness of solutions. Finally, the global attractor is proved to exist.