Analytic study of differential equations

微分方程的解析研究

• 批准号: 60302007
• 负责人: KIMURA Tosihusa
• 金额: $ 3.52万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60302007/
• 关键词: Ordinary differential equation; total differential equation; Partial differential equation; Isomonodromic deformation; Painleve systems; Elliptic; Hyperbolic; 有界性; 楕円型; 双曲型; 放物型; 初期問題; 境界値問題; 混合問題; 特異性の伝播; Govrey級; マイクロローカル

The aim of this project is to research differential equations, ordinary, total and partial, and functional equations related to the equations above in an analytic method. Many results are obtained for each class of the equations. We state main results for ordinary and total differential equations. Head investigator T. Kimura considered a completely integrable system of partial differential equations with polynomial coefficients in two independent variables, and supposing that the solution space of the system is of dimension 3, studied the map <C^2> - <P^2> (C) obtained from 3 independent solutions. This research is the first step to a 2-dimensional case from a 1-dimensional case related to ordinary differential equation. Then Kimura studied Fatou-Bieberbach domains in <C^2> . Investigator K. Okamoto made very active researches. He studied the isomonodromic deformation for a second order ordinary differential equation containing several deformation parameters and discovered an algorithm of deriving deformation equations for higher order equations. He investigated the theory of transformations making the Painleve systems invariant and determined the transformation groups for the Painleve systems <II> - <VI> . Investigator M. Yoshida also made active researches. He derived uniformizing differential equations for orbifolds uniformized by Hermite symmetric spaces.

该项目的目的是研究与以上方程相关的分析方法中的平方，总和部分以及功能方程式的微分方程。每个方程式都能获得许多结果。我们陈述了普通和总分方程的主要结果。头部研究员T. kimura认为在两个独立变量中具有多项式系数的部分偏微分方程的完全可以整合的系统，并认为系统的溶液空间是维度3的，研究了地图<c^2> - <p^2>（c），从3个独立的解决方案中获得。这项研究是与普通微分方程有关的一维情况的二维情况的第一步。然后，木村在<c^2>中研究了Fatou-Bieberbach域。研究人员K. Okamoto进行了非常积极的研究。他研究了一个二阶的普通微分方程，该方程包含多个变形参数，并发现了一种用于高阶方程的变形方程的算法。他调查了使潘leve系统不变的转化理论，并确定了潘leve系统<ii> - <vi>的转换组。研究人员M. Yoshida还进行了积极的研究。他衍生出均匀的差分方程，以构成由Hermite对称空间均匀的Orbifolds。

项目成果

Junji Kato: "An asymptotic estimation of a function satisfying a differential inequality." J. Math. Anal. & Appl.118. 151-156 (1986)

Junji Kato：“满足微分不等式的函数的渐近估计。”

小野昭: Funkc.Ekvac.28. 83-92 (1985)

小野晃：Funkc.Ekvac.28（1985）。

木村俊房: preprint series 87-1,Dept.Math.,Univ.Tokyo. 1-63 (1987)

木村俊房：预印本系列 87-1，东京大学数学系 1-63 (1987)。

加藤順二: J.Math.Anal.of Appl.118. 151-156 (1986)

加藤淳二：J.Math.Anal.of Appl.151-156 (1986)。

Masaaki Yoshida: Vieweg. Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory., 214 (1987)

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