| 有阻尼受迫sine-Gordon方程的全局周期吸引子 |
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| 引用本文： | 洙澍,周盛凡. 有阻尼受迫sine-Gordon方程的全局周期吸引子[J]. 数学学报, 1999, 42(5): 809-814. DOI: cnki:ISSN:0583-1431.0.1999-05-005 |
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| 作者姓名： | 洙澍 周盛凡 |
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| 作者单位： | 1. 北京大学数学系 北京 100871
2. 四川大学数学系,成都,610064 |
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| 摘 要： | 本文证明了当阻尼与扩散系数在一定的参数范围内时，有阻尼的受迫sineGordon方程的狄氏问题对于任意非自治时间周期受迫力均具有唯一的指数吸引有界集的周期解．并且，如果受迫力是自治的，则全局吸引子恰是系统唯一的指数吸引有界集的平衡解．
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| 关 键 词： | sine-Gordon方程 周期解 平衡解 Mora范数 |
| 修稿时间： | :1998-01-2 |
Global Periodic Attrector for the Damped and Driven sine-Gordon Equation |
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| Zhu Shu,Zhou Shengfan. Global Periodic Attrector for the Damped and Driven sine-Gordon Equation[J]. Acta Mathematica Sinica, 1999, 42(5): 809-814. DOI: cnki:ISSN:0583-1431.0.1999-05-005 |
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| Authors: | Zhu Shu Zhou Shengfan |
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| Affiliation: | Zhu Shu (Department of Mathematics, Peking University, Beijing 100871, P. R. China)Zhou Shengfan (Department of Mathemotics, Sichuan University, Chengdu 610064, P. R. China) |
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| Abstract: | This paper studies the damped and driven sine-Gordon equation with homogeneous Dirichlet boundary conditions. It is shown that in certain parameter region of damping and diffusing, for arbitrary nonautonomous and time-periodic driving force, the system has a unique periodic solution, which attracts any bounded set exponentially. Moreover, if the driving force is autonomous, the global attractor consists of only the unique equilibrium point which attracts any bounded set exponentially. |
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| Keywords: | sine-Gordon equation Periodic solution Equilibrium solution Mora norm |
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