| 摘要: |
| 本文研究了非线性柯西问题的适定性问题.利用经典的能量法和抽象柯西-柯瓦列夫斯卡娅定理，得到非线性柯西问题在Gevrey空间中是适定的.推广了已有文献在非线性柯西问题适定性方面的研究. |
| 关键词: 柯西-柯瓦列夫斯卡娅定理 Gevrey空间 能量法 柯西问题 |
| DOI： |
| 分类号:O175.4 |
| 基金项目: |
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| ABSTRACT CAUCHY-KOVALEVSKAYA THEOREM IN GEVREY SPACE: ENERGY METHOD |
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CHEN Jun-ling
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School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
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| Abstract: |
| In this paper, we study the well-posedness of nonlinear Cauchy problem. The main tool is the combination of the classical energy method and abstract Cauchy-Kovalevskaya Theorem. We obtain that the nonlinear Cauchy problem is well-posed in the Gevrey space, which is an extension on the existing literature in the aspect of well-posedness for the nonlinear Cauchy problem. |
| Key words: Cauchy-Kovalevakaya theorem Gevrey space energy method Cauchy problem |
