1986 Fiscal Year Final Research Report Summary
Analytic study of differential equations
| Project/Area Number |
60302007
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | University of Tokyo |
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Principal Investigator |
KIMURA Tosihusa Dept. of Math., Fac. of Sci., Univ. of Tokyo, Professor, 理学部, 教授 (50011466)
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| Co-Investigator(Kenkyū-buntansha) |
ONO Akira Dept. of Math., Fac. of Science, Kyushu Univ., Professor, 教養部, 教授 (80038405)
TANABE Hiroki Dept. of Math., Fac. of Science, Osaka University, Professor, 理学部, 教授 (70028083)
MATSUMURA Mutsuhide Inst. of Math., Univ. of Tsukuba, Professor, 数学系, 教授 (30025879)
KUSANO Takasi Dept. of Math., Fac. of Science, Hiroshima Univ., Professor, 理学部, 教授 (70033868)
KATO Junji Dept. of Math., Fac. of Science, Tohoku Univ., Professor, 理学部, 教授 (80004290)
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| Project Period (FY) |
1985 – 1986
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| Keywords | 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 |
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| Research Abstract |
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.
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