| Sine—Gordon方程的全局吸引子的维数估计 |
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| 引用本文： | 周盛凡.Sine—Gordon方程的全局吸引子的维数估计[J].应用数学学报,1998,21(3):445-450. |
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| 作者姓名： | 周盛凡 |
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| 作者单位： | 四川联合大学数学系!成都，610064 |
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| 摘 要： | 本文得到了阻尼Ｓｉｎｅ－Ｇｏｒｄｏｎ方程的狄氏问题的全局吸引子的Ｈａｕｓｄｏｒｆｆ维数以偶数上界的参数条件，特别地，当阻尼与Ｌａｐｌａｅ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。
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| 关 键 词： | 全局吸引子 维数 估计 S－G方程 豪斯道夫维数 |
ESTIMATE OF DIMENSION OF THE GLOBAL ATTRACTOR FOR SINE-GORDON EQUATION |
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| ZHOU SHENFAN.ESTIMATE OF DIMENSION OF THE GLOBAL ATTRACTOR FOR SINE-GORDON EQUATION[J].Acta Mathematicae Applicatae Sinica,1998,21(3):445-450. |
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| Authors: | ZHOU SHENFAN |
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| Abstract: | 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. |
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| Keywords: | Sine-Gordon equation global attractor Mora norm Hausdorff dimension |
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