| KdV-Burgers-Kuramoto系统的渐近吸引子 |
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| 引用本文： | 张晓明,姜金平,董超雨.KdV-Burgers-Kuramoto系统的渐近吸引子[J].纯粹数学与应用数学,2014(6):595-603. |
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| 作者姓名： | 张晓明 姜金平 董超雨 |
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| 作者单位： | 延安大学数学与计算机科学学院,陕西 延安,716000 |
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| 基金项目： | 国家自然科学基金，陕西省科技计划项目，延安市科技计划项目，延安大学研究生教育创新计划项目 |
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| 摘 要： | 研究了 KdV-Burgers-Kuramoto 方程的渐近吸引子，即利用正交分解法构造一个有限维解序列。首先用数学归纳法证明了该解序列不会远离方程的整体吸引子，接着证明解序列在长时间后无限趋于方程的整体吸引子，最后给出渐近吸引子的维数估计。
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| 关 键 词： | KdV-Burgers-Kuramoto方程 解序列 渐近吸引子 维数估计 |
Asymptotic attractor of KdV-Burgers-Kuramoto equation |
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| Zhang Xiaoming,Jiang Jinping,Dong Chaoyu.Asymptotic attractor of KdV-Burgers-Kuramoto equation[J].Pure and Applied Mathematics,2014(6):595-603. |
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| Authors: | Zhang Xiaoming Jiang Jinping Dong Chaoyu |
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| Institution: | (College of Mathematics and Computer Science, Yan＇an University, Yan＇an 716000, China) |
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| Abstract: | In this paper, we study the asymptotic attractor of KdV-Burgers-Kuramoto equations. A solution sequence is constructed by using orthogonal decomposition. It is shown that the solution sequence doesn′t go away from the global attractor in terms of mathematical induction. Then it is obtained that the solution sequence approaches to the global attractor of the equation in long time and the dimensional estimate of the asymptotic attractor is obtained. |
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| Keywords: | KdV-Burgers-Kuramoto equation solution sequence asymptotic attractor dimensional estimate |
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