Structure of the Solutions to Partial Differential Equations Degenerating on the Initial Surface

初表面上退化的偏微分方程解的结构

• 批准号: 10640157
• 负责人: MANDAI Takeshi
• 金额: $ 2.43万
• 依托单位: Osaka Electro-Communication University (1999)Gifu University (1998)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640157/
• 关键词: Fuchsian partial differential equations; regular singularity; method of Frobenius; characteristic exponent; characteristic Cauchy problem; フックス型偏微分作用素; ワックス型偏微分作用素

The Indicial polynomial and its zero called characteristic exponent play an important role in the study of Fuchsian partial differential equations in the sense of Baouendi-Goulaouic, that is, linear partial differential equations with regular singularity along the initial surface. Some conditions on the indicial polynomial have been assumed in most of the results. Mainly, we aimed to consider Fuchsian equations without any assumptions on the indicial polynomial. The main results are the following.First, we could construct a solution map which gives the local structure the solutions to homogeneous single Fuchsian partial differential equations in a complex domain. We also had a similar result for Fuchsian systems of homogeneous equations.We could also construct a solution to inhomogeneous Fuchsian equations, which is 'near' to a holomorphic solution.Our idea seems to be applicable to wider range of problems, and we have already some results of extensions.

在Baouendi-goulaouic的意义上，指示性多项式及其零称为特征指数在研究紫色部分微分方程的研究中起着重要作用，即，线性偏微分方程在初始表面具有正常的奇异性。在大多数结果中都假定了指示性多项式的某些条件。主要是，我们旨在考虑fuchsian方程，而无需对指示多项式的任何假设。主要结果是以下结果。首先，我们可以构建一个解决方案映射，该映射为局部结构提供了复杂域中均匀的单一偏射偏微分方程的解决方案。我们对均匀方程式的Fuchsian系统也有类似的结果。我们还可以构建解决方案的解决方案，该方程与Holomorthic solution“接近”。我们的想法似乎适用于更广泛的问题，我们已经适用扩展的一些结果。

项目成果

Takeshi MANDAI: "The Method of Frobenius to Fuchsian Partial Differentcal Eguations"Journal of Mathematical Society of Japan. (to appear).

Takeshi MANDAI：“Frobenius 的 Fuchsian 偏微分方程的方法”日本数学会杂志。

Takeshi MANDAI: "The Method of Frobenius to Fuchsian Partial Differential Equations"J. Math. Soc. Japan. (to appear).

Takeshi MANDAI：“Frobenius 求解 Fuchs 偏微分方程的方法”J。

Takeshi MANDAI: "The Method of Frobenius to Fuchsian Partial Differential Equations"Journal of Math.Soc.Japan. (to appear).

Takeshi MANDAI：“Frobenius 求解 Fuchsian 偏微分方程的方法”Journal of Math.Soc.Japan。