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.
出处
《应用数学学报》
CSCD
北大核心
1998年第3期445-450,共6页
Acta Mathematicae Applicatae Sinica
