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| 修正Camassa-Holm方程的Cauchy问题 | |
| 引用本文： | 张双虎,冯兆永,杨凯波.修正Camassa-Holm方程的Cauchy问题[J].中山大学学报(自然科学版),2014,53(4):8-12. |
| 作者姓名： | 张双虎 冯兆永 杨凯波 |
| 作者单位： | 1．西南大学数学与统计学院, 重庆 400715; 2．中山大学数学与计算科学学院, 广东 广州 510275 |
| 基金项目： | 国家自然科学基金资助项目(11101337);教育部新教师博士点基金资助项目(20110182120013);中央高校基本科研业务费专项资金资助项目(XDJK2011C046);西南大学博士基金资助项目(SWU110035) |
| 摘 要： | 主要研究修正Camassa-Holm方程的Cauchy问题。首先提出了一个新的爆破结果,这一结果优化了早先获得的一些结果;然后证明了修正Camassa-Holm方程的Cauchy问题在解对初值不一致连续依赖意义下在空间H~3(R),s3/2中不适定。 |
| 关 键 词： | 修正CamassaHolm方程 爆破 关于初值非一致依赖性 |
| 收稿时间： | 2014-01-29; |
The Cauchy Problem for the Modified Camassa-Holm Equations |
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| ZHANG Shuanghu,FENG Zhaoyong,YANG Kaibo.The Cauchy Problem for the Modified Camassa-Holm Equations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2014,53(4):8-12. | |
| Authors: | ZHANG Shuanghu FENG Zhaoyong YANG Kaibo |
| Institution: | 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China; 2. School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China |
| Abstract: | The Cauchy problem of the modified Camassa-Holm equation is mainly studied. First, a new blow-up phenomenon which is an improvement of the earlier ones is presented. Then it is proved that the Cauchy problem for the modified Camassa-Holm equation is not locally well-posedness in the sense that its solution does not depend uniformly continuously on the initial data. |
| Keywords: | the modified Camassa-Holm equation blow up non-uniform dependence on initial data |
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