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

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.