高维复域中具非正则奇异性的非线性偏微分方程的形式解

顾素萍, 罗壮初, 陈化

数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 897-904.

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数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 897-904. DOI: 10.12386/A2010sxxb0100
论文

高维复域中具非正则奇异性的非线性偏微分方程的形式解

    顾素萍, 罗壮初, 陈化
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Formal Solutions for First Order Nonlinear PDE with Irregular Singularity in High Dimensional Complex Domain

    Su Ping GU, Zhuang Chu LUO, Hua CHEN
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摘要

本文在上研究一类一阶具非正则奇异性的非线性偏微分方程.在一定条件下, 证明了其形式幂级数解 属于形式Gevrey类,并给出了其Gevrey类指标的精确刻画.  

Abstract

In this paper, we study a class of first order nonlinear partial differential equation with irregular singularity in the domain . Under certain assumptions, we prove the existence and uniqueness of the formal solution in formal Gevrey class.  

关键词

奇异偏微分方程 / 形式解 / 形式Gevrey类

Key words

singular partial differential equation / formal solution / formal Gevrey class

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顾素萍, 罗壮初, 陈化. 高维复域中具非正则奇异性的非线性偏微分方程的形式解. 数学学报, 2010, 53(5): 897-904 https://doi.org/10.12386/A2010sxxb0100
Su Ping GU, Zhuang Chu LUO, Hua CHEN. Formal Solutions for First Order Nonlinear PDE with Irregular Singularity in High Dimensional Complex Domain. Acta Mathematica Sinica, Chinese Series, 2010, 53(5): 897-904 https://doi.org/10.12386/A2010sxxb0100

参考文献



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[10] Chen H., Luo Z., Formal Solutions for Higher Order Nonlinear Totally Characteristic PDEs with Irregular Singularities, Geometric Analysis of PDE and Several Complex Variables, 121--131, Contemp. Math., 368, Amer. Math. Soc., Providence, RI, 2005.



[11] Hörmmander L., Linear Partial Differential Operators, Springer, 1963.

基金

国家自然科学基金资助项目(10401028)

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