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Analytic study of differential equations

Research Project

Project/Area Number 60302007
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionUniversity of Tokyo

Principal Investigator

KIMURA Tosihusa  Dept. of Math., Fac. of Sci., Univ. of Tokyo, Professor, 理学部, 教授 (50011466)

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)
Project Period (FY) 1985 – 1986
Project Status Completed (Fiscal Year 1986)
Budget Amount *help
¥5,500,000 (Direct Cost: ¥5,500,000)
Fiscal Year 1986: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1985: ¥2,800,000 (Direct Cost: ¥2,800,000)
KeywordsOrdinary 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
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.

Report

(1 results)
  • 1986 Final Research Report Summary
  • Research Products

    (13 results)

All Other

All Publications (13 results)

  • [Publications] 木村俊房: Acte du【4^e】colloque franco-japonais,Equationsdifferentielles dans le champ complexe. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 木村俊房: preprint series 87-1,Dept.Math.,Univ.Tokyo. 1-63 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 加藤順二: J.Math.Anal.of Appl.118. 151-156 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 草野尚,W.F.Trench: J.London Math.Soc.31. 478-486 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 田辺広城: J.Fac.Sci.Univ.Tokyo. 34. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 小野昭: Funkc.Ekvac.28. 83-92 (1985)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] 吉田正章: "Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory" Vieweg, 214 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Tosihusa Kimura: "Maps with polynomial Schwarzian derivatives and the Jacobian problem." Acte du <4^e> colloque franco-japonais, Equations differentielles dans le champ complexe. (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Akira Ono: "Morrey-Sobolevetype imbedding theorems in the spaces of strong type." Funkc. Ekvac.28. 83-92 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Junji Kato: "An asymptotic estimation of a function satisfying a differential inequality." J. Math. Anal. & Appl.118. 151-156 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Takasi Kusano (with W.F. Trench): "Global existence theorems for solutions of nonlinear differential equations with prescribed asymptotic behavior." J. London Math. Soc.31. 478-486 (1985)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Hiroki Tanabe: "Volterra integro-differential equations of pqrabolic type of higher order in t." J. Fac. Sci.,Univ. Tokyo. 34. (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Masaaki Yoshida: Vieweg. Fuchsian differential equations with special emphasis on the Gauss-Schwarz theory., 214 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary

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Published: 1987-03-31   Modified: 2016-04-21  

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