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Borel summability of divergent solutions of differential equations and the structure of its Borel sum

Research Project

Project/Area Number 19740091
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionKanagawa Institute of Technology

Principal Investigator

ICHINOBE Kunio  Kanagawa Institute of Technology, 基礎・教養教育センター, 准教授 (20434417)

Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥1,250,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥600,000 (Direct Cost: ¥600,000)
Keywords偏微分方程式 / 発散級数 / ボレル総和法 / 初期値問題 / 常微分方程式系 / 不確定度 / 発散級数解
Research Abstract

1.非コワレフ型偏微分方程式の初期値問題に対する発散解のボレル総和可能性について、特殊な作用素の場合、非斉次方程式に帰着し、未知の発散解を既知の発散解を用いて与えることが出来る。これにより、未知発散解の性質は既知発散解の性質と同様であることが判る。後は方程式の拡張が残された問題である。2.不確定特異点を持つ常微分方程式系の解に対する指数増大評価の指数によって不確定度を定義し、この不確定度を係数行列の零点の平均の位数を用いることにより特徴付けた。

Report

(3 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report

Research Products

(9 results)

All 2009 2008 2007

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (7 results)

  • [Journal Article] Irregularity for singular system of ordinary differential equations in complex domain2009

    • Author(s)
      三宅正武、市延邦夫
    • Journal Title

      Funkcialaj Ekvacioj 52(2009)

      Pages: 53-82

    • NAID

      130000140722

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Irregularity for singular system of ordinary differential equations in complex domain2009

    • Author(s)
      K. Ichinobe
    • Journal Title

      FUNKCIALAJ EKVACIOJ 52

      Pages: 53-82

    • NAID

      130000140722

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] On the characterization of Irregularity for singular system of ordinary differential equations in complex domain2008

    • Author(s)
      市延邦夫
    • Organizer
      Global Behaviors of Differential Equations-Singularity and Transformation Theory-
    • Place of Presentation
      広島大学・理学研究科
    • Year and Date
      2008-09-09
    • Related Report
      2008 Final Research Report
  • [Presentation] On the Characterization of Irregularity for Singular System of Ordinary Differential Equations in Complex Domain2008

    • Author(s)
      K. Ichinobe
    • Organizer
      International Workshop on Global Behaviors of Differential Equations
    • Place of Presentation
      広島大学理学研究科
    • Year and Date
      2008-09-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] Characterization of Irregularity for singular system of ordinary differential equations in complex domain2008

    • Author(s)
      市延邦夫
    • Organizer
      Formal and Analytic Solutions of Differential Equations
    • Place of Presentation
      Banach International Mathematical Center(Poland)
    • Year and Date
      2008-08-11
    • Related Report
      2008 Final Research Report
  • [Presentation] Characterization of Irregularity for singular system of ordinary differential equations in complex domain2008

    • Author(s)
      K. Ichinobe
    • Organizer
      Formal and Analytic Solutions of Differential Equations
    • Place of Presentation
      ポーランド・ポズナニ
    • Year and Date
      2008-08-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Characterization of Irregularity for singular system of ordinary differential equations in complex domain2008

    • Author(s)
      市延邦夫
    • Organizer
      Exact WKB Analysis and Microlocal Analysis
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-05-30
    • Related Report
      2008 Final Research Report
  • [Presentation] Irregularity for singular system of ordinary differential equations in complex domain2008

    • Author(s)
      K. Ichinobe
    • Organizer
      完全WKB解析と超局所解析
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-05-30
    • Related Report
      2008 Annual Research Report
  • [Presentation] Decomposition of Solutions of the Cauchy problem for a Quasi Homogeneous Partial Differential Operator with Constant Coefficients2007

    • Author(s)
      市延 邦夫
    • Organizer
      ドイツ、ウルム大学・トゥリエール大学合同研究集会
    • Place of Presentation
      イタリア・コルフォスコ
    • Year and Date
      2007-09-10
    • Related Report
      2007 Annual Research Report

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Published: 2007-03-31   Modified: 2016-04-21  

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