非齐次边界条件下Sine-Gordon型二阶非线性系统的全局吸引子及能稳性  

The Global Attractor of the Sine-Gordon Type Nonlinear Second Order System Under Nonhomogeneous Boundary Condition and the Stabilizability

作　　者：李全国[1] 

机构地区：[1]暨南大学数学系,广州510632

出　　处：《应用数学学报》2006年第6期1118-1124,共7页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(60474048号)资助项目.

摘　　要：本文在非齐次边界条件下,证明了有阻尼Sine-Gordon型二阶非线性系统的全局吸引子的存在性．同时证明了当时,该全局吸引子为—个平衡点,而且该平衡点具有指数吸引性．并将所得结果应用到系统能稳性的研究中．Abstract This paper proves the existences of the global attractor of the Sine- Gordon type nonlinear second order system under nonhmomgeneous boundary condition, at the same time, the global attractor is proved to be a equilibrium point when ｜β｜〈λ1 1/2ε＇（ε＇=min（α/4,λ/2α,√λ1/2））, and the equilibrium point is exponentially attractive. The result is applied to the study of the stabilizability of system.

关 键 词：SINE-GORDON方程 平衡点 全局吸引子 变分法 

分 类 号：O19[理学—数学] O23[理学—基础数学]