| 非自治Ginzburg-Landau方程的周期解和全局周期吸引子 |
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| 引用本文： | 吴书印,赵怡.非自治Ginzburg-Landau方程的周期解和全局周期吸引子[J].应用泛函分析学报,2005,7(2):123-129. |
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| 作者姓名： | 吴书印 赵怡 |
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| 作者单位： | 1. 中山大学计算机科学系,广东,广州,510275
2. 中山大学数学系,广东,广州,510275 |
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| 基金项目： | SupportedbytheNationalNaturalScienceFoundationofChina(10371136) |
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| 摘 要： | 研究受周期外力影响的非自治Ginzburg-Landau方程的解的长时间行为.首先证明系统在空间H上存在周期解,而且周期解包含在空间V中的一个有界吸收集内.然后证明了当耗散系数λ满足一定条件时,该系统在空间H上具有唯一的周期解,该周期解指数吸引H中的任意有界集.
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| 关 键 词： | 非自治Ginzburg-Landau方程 Poincaré映射 周期解 全局周期吸引子 |
| 文章编号： | 1009-1327（2005）02-0123-07 |
| 修稿时间： | 2003年3月13日 |
Periodic Solution and Global Periodic Attractor for the Nonautonomous Ginzburg-Landau Equation |
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| WU Shu-yin,ZHAO Yi.Periodic Solution and Global Periodic Attractor for the Nonautonomous Ginzburg-Landau Equation[J].Acta Analysis Functionalis Applicata,2005,7(2):123-129. |
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| Authors: | WU Shu-yin ZHAO Yi |
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| Institution: | WU Shu-yin1,ZHAO Yi2[JZ)]1. Department of Computer Science,Zhongshan University,Guangzhou 510275,China2. Department of Mathematics,Zhongshan University,Guangzhou 510275,China |
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| Abstract: | We study the long time behavior of solutions for the nonautonomous Ginzburg-Landau equation driven by a time-periodic force. It is shown that the system has periodic solutions in the space H and the periodic solutions are included in a bounded absorbing set in the space V. Moreover,if the dissipative parameter λ is in certain range, the system has a unique periodic solution in H,which attracts any bounded set in H exponentially. |
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| Keywords: | nonautonomous Ginzburg-Landau equation Poincare map periodic solution global periodic attractor |
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