Global Attractor for KGS Lattice System
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摘要: 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.Abstract: The longtime behavior of solutions of a coupled lattice dynamical system of Klein-Gordon Schrêdinger 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 D-entropy of the global attractor is estimated by applying element decomposition and the covering property of a polyhedron by balls of radii D in the finite dimensional space.Finally,an approximation to the global attractor is presented by the global attractors of finitedimensional ordinary differential systems.
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