| 有阻尼Sine－Gordon方程的全局吸引子的维数 |
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| 引用本文： | 周盛凡. 有阻尼Sine－Gordon方程的全局吸引子的维数[J]. 数学学报, 1996, 39(5). DOI: cnki:ISSN:05831431.0.1996-05-003 |
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| 作者姓名： | 周盛凡 |
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| 作者单位： | 四川大学数学系 |
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| 摘 要： | 本文通过引入新范数，得到有阻尼Ｓｉｎｅ－Ｇｏｒｄｏｎ方程的Ｄｉｒｉｃｈｌｅｔ问题的全局吸引子的维数的一个估计．结果表明：当“阻尼”与“扩散”同时增大或正弦项系数减小时，吸引子的维数减小．特别地，得到了零维吸引子存在的参数条件．
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| 关 键 词： | Sine－Gordon方程，全局吸引子，Hausdorff维数 |
| 收稿时间： | 1995-03-13 |
Dimension of the Global Attractor for the Damped Sine-Gordon Equation |
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| Zhou Shengfan. Dimension of the Global Attractor for the Damped Sine-Gordon Equation[J]. Acta Mathematica Sinica, 1996, 39(5). DOI: cnki:ISSN:05831431.0.1996-05-003 |
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| Authors: | Zhou Shengfan |
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| Affiliation: | Zhou Shengfan(Department of Mathematics,Sichuan University, Chengdu 610064, China) |
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| Abstract: | An estimate of dimension of the global attractor for the damped Sine-Gordon equation with homogeneous Dirichlet boundary condition is obtained by introducing a new norm.This estimate shows that the Hausdorff dimension of the global attractor decreases when both the "damping" and the "diffusing" increase or the coefficient of the Sine term decreases.In particular, under certain conditions,the dimension is zero. |
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| Keywords: | Sine-Gordon equation Global attractor Hausdorff dimension |
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