| 非线性全特征型偏微分方程组的全纯解 |
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| 引用本文： | 孙丞,陈化.非线性全特征型偏微分方程组的全纯解[J].数学年刊A辑(中文版),2004(1). |
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| 作者姓名： | 孙丞 陈化 |
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| 作者单位： | 武汉大学数学与统计学院，武汉大学数学与统计学院 武汉 430072，武汉 430072 |
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| 基金项目： | 国家自然科学基金(No.19531080)，973项目(No.G1999075107)资助的课题 |
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| 摘 要： | 本文在复空间C_t×C_x上讨论了一类非线性全特征型具正则奇性偏微分方程组的全纯解,在一定的条件下,证明了在复空C_t×C_x的原点附近的某个邻域内存在唯一的全纯解,并把结论推广到了高阶的情况.本文的结果实际上是经典的Cauchy-Kowalewski定理在非线性奇异方程组上的推广。
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| 关 键 词： | 非线性 奇异偏微分方程组 全纯解 |
ON THE HOLOMORPHIC SOLUTIONS FOR THE NONLINEAR TOTALLY CHARACTERISTIC SYSTEMS |
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| SUN Cheng CHEN Hua
School of Mathematics and Statistics,Wuhan University,Wuhan ,China..ON THE HOLOMORPHIC SOLUTIONS FOR THE NONLINEAR TOTALLY CHARACTERISTIC SYSTEMS[J].Chinese Annals of Mathematics,2004(1). |
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| Authors: | SUN Cheng CHEN Hua
School of Mathematics and Statistics Wuhan University Wuhan China |
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| Institution: | SUN Cheng CHEN Hua
School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China. |
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| Abstract: | This paper studies a class of non-linear singular partial differential systems denned on the complex domain. Under the certain assumptions, The authors prove the existence and uniqueness of the local holomorphic solution for the system and extend the result to the case of high order system. This result is actually extension of the classical Cauchy-Kowalewski Theorem to the nonlinear singular systems. |
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| Keywords: | Non-linear Singular partial differential system Holomorphic solution |
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