Sine-Gordon方程的全局吸引子的维数估计  

ESTIMATE OF DIMENSION OF THE GLOBAL ATTRACTOR FOR SINE-GORDON EQUATION

作　　者：周盛凡[1] 

机构地区：[1]四川联合大学数学系,成都610064

出　　处：《应用数学学报》1998年第3期445-450,共6页Acta Mathematicae Applicatae Sinica

摘　　要：本文得到了有阻尼Sine－Gordon方程的狄氏问题的全局吸引子的Hausdorff维数以偶数为上界的参数条件．特别地，当阻尼与Laplace算子的第一个特征值适当大时，全局吸引子是零维的，零维吸引子恰是系统的唯一平衡解并且指数吸引相空间的有界集．In this paper, we obtain a parameter region in which the Hausdorff dimensionof the global attractor for damped sine-Gordon equation with Dirichlet boundary conditionis bounded by even number. Particularly, if the damping and the first eigenvalue of Laplaceoperator are suitable large, the global attractor is zero-dimensional, and the zero-dimensionalattractor is exactly the unique equilibrium solution of system which attracts any boundedset of phase space exponentially.

关 键 词：全局吸引子 维数 估计 S-G方程 豪斯道夫维数 

分 类 号：O175.2[理学—数学]