| 非正则奇异性偏微分方程组的形式解 |
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| 引用本文： | 顾素萍,陈化,罗壮初. 非正则奇异性偏微分方程组的形式解[J]. 数学杂志, 2012, 32(4): 729-739 |
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| 作者姓名： | 顾素萍 陈化 罗壮初 |
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| 作者单位： | 武汉大学数学与统计学院,湖北武汉,430072 |
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| 摘 要： | 本文研究了在复空间Ct×Cx上一类具有非正则奇异性的偏微分方程组的问题.利用形式Borel变换的方法,在一定的条件下,获得了在复空间Ct×Cx的原点附近的某个邻域内存在唯一的形式解,且该形式解属于某Gevery类,并给出了该Gevery类的指标,推广了非正则奇异性偏微分方程的研究结果.
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| 关 键 词： | 方程组 奇异偏微分方程 形式解 Gevrey类 |
FORMAL SOLUTIONS FOR FIRST ORDER NONLINEAR PDES WITH IRREGULAR SINGULARITY |
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| GU Su-ping , CHEN Hua , LUO Zhuang-chu. FORMAL SOLUTIONS FOR FIRST ORDER NONLINEAR PDES WITH IRREGULAR SINGULARITY[J]. Journal of Mathematics, 2012, 32(4): 729-739 |
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| Authors: | GU Su-ping CHEN Hua LUO Zhuang-chu |
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| Affiliation: | (School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China) |
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| Abstract: | In this paper,we study a class of first order nonlinear partial differential equations with irregular singularity in the domain Ct × Cx.By using formal Borel transformation,we prove the existence and uniqueness of the formal solution in formal Gevrey class under certain assumptions,which extend the result of nonlinear partial differential equation with irregular singularity. |
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| Keywords: | partial differential equations singular partial differential equation formal solution Gevrey class |
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