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

Research Project

Project/Area Number 10640157
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka Electro-Communication University (1999)
Gifu University (1998)

Principal Investigator

MANDAI Takeshi  Osaka Electro-Communication University, Faculty of Engineering, Professor, 工学部, 教授 (10181843)

Co-Investigator(Kenkyū-buntansha) IGARI Katsuju  Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (90025487)
SHIGA Kiyoshi  Gifu University, Faculty of Engineering, Professor, 工学部, 教授 (10022683)
TAHARA Hidetoshi  Sophia University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (60101028)
SAKATA Sadahisa  Osaka Electro-Communication University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60175362)
YAMAHARA Hideo  Osaka Electro-Communication University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30103344)
浅倉 史興  大阪電気通信大学, 工学部, 教授 (20140238)
浅川 秀一  岐阜大学, 工学部, 助手 (00211003)
室 政和  岐阜大学, 工学部, 教授 (70127934)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1999: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1998: ¥1,900,000 (Direct Cost: ¥1,900,000)
KeywordsFuchsian 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
Research Abstract

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.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (3 results)

All Other

All Publications (3 results)

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

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takeshi MANDAI: "The Method of Frobenius to Fuchsian Partial Differential Equations"J. Math. Soc. Japan. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takeshi MANDAI: "The Method of Frobenius to Fuchsian Partial Differential Equations"Journal of Math.Soc.Japan. (to appear).

    • Related Report
      1999 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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