KGS格点系统的全局吸引子

Global Attractor for KGS Lattice System

考虑了对应于Klein-Gordon-Schrdinger方程的格点系统(KGS格点系统)的解的长时间行为.首先通过引入一个加权范数与采用解的“切尾”法,证明了全局吸引子的存在性.在此基础上,采用元素分解法与多面体的球覆盖性质,得到了此吸引子的Kolmogorov δ-熵的上界的一个估计.最后,我们用有限维的常微分方程的全局吸引子逼近它.

The longtime behavior of solutions of a coupled lattice dynamical system of Klein-Gordon-Schrdinger equation（KGS lattice system）was considered.The existence of a global attractor for the system is proved here by introducing an equivalent norm and using ＂End Tails＂ of solutions.Then the upper bound of the Kolmogorov δ-entropy of the global attractor is estimated by applying element decomposition and the covering property of a polyhedron by balls of radii δ in the finite dimensional space.Finally,an approximation to the global attractor is presented by the global attractors of finite-dimenmonal ordinary clifferential systems.