一类Sine-Gordon型二阶非线性系统全局吸引子的退化条件及能稳性  

THE REDUCTION CONDITIONS OF THE GLOBAL ATTRACTOR FOR A CLASS OF NONLINEAR SECOND ORDER SYSTEMS AND THE STABILIZABILITY

作　　者：赵怡[1] 李全国[1] 

机构地区：[1]中山大学数学系,广州510275

出　　处：《系统科学与数学》1999年第2期205-210,共6页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金;广东省自然科学基金

摘　　要：本文证明了当｜β｜＜时，有阻尼Sine－Gordon方程的Dirichlet问题的全局吸引子为一个平衡点，而且该平衡点具有指数吸引性，同时将所得结果应用到系统能稳性的研究中．最后给出了若干一般性的结果．This paper proves that the global attractor of the damped Sine-Gordon equation with homogenous Dirichlet boundary condition reduces to an equilibrium point when and the equilibrium point is exponentially attractive.At the same time, the result is applied to the study of the stabilizability of the system. More general results are given at the end of the paper.

关 键 词：S-G方程 全局吸引子 非线性系统 退化条件 

分 类 号：O175.29[理学—数学]