• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study of partial differential equations and tomography by microlocal and discrete methods

Research Project

Project/Area Number 20540157
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOchanomizu University

Principal Investigator

KANEKO Akira  お茶の水女子大学, 名誉教授 (30011654)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords代数解析 / 偏微分方程式 / トモグラフィー / 半線型熱方程式 / 藤田現象 / 爆発の臨界指数 / 2方向投影データトモグラフィ / 電荷分布の形状同定 / 解の爆発 / トモグラフィ / 逆問題 / 電荷分布の同定 / ニュートン法 / Fredholm型積分方程式 / f半線型熱方程式 / 離散トモグラフィ / 電荷分布の逆問題 / 解の爆発の臨界指数 / スイッチンググラフ
Research Abstract

We studied on various problems of partial differential equations and tomography by means of microlocal and discrete approach. Especially we got new interesting results on the critical exponent of blowup of semilinear heat equation with logarithmic nonlinearity by determining the critical exponent for generalized paraboloidal domain, and on the switching graph of solution sets of 2 projection tomography which is a means of studying non-uniqueness of solution, by enumerating them up to order 20 with aid of theoretical consideration and computer experiment.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (27 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (10 results) (of which Peer Reviewed: 6 results) Presentation (15 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Second Critical Exponent of Blowup for Heat Equation with Power-logarithm Nonlinearity on Paraboloidally Perturbed Conical Domain2011

    • Author(s)
      Akira Kaneko, Shie Nishikawa
    • Journal Title

      Technical Report OCHA-IS

      Volume: 11-2 Pages: 1-6

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Identification of the shape of curvilinear charge distribution2010

    • Author(s)
      Akira KANEKO, Toshiko KANESHIGE
    • Journal Title

      Technical Report Ocha-IS 10-1

      Pages: 1-5

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Criticalexponent of blowup for heat equation with logarithmic nonlinearity on paraboloidaldomain2009

    • Author(s)
      Akira Kaneko, Shie Nishikawa
    • Journal Title

      Nat. Sci. Report Ochanomizu Univ.

      Volume: 60-1 Pages: 1-13

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Enumeration of switching graphs of smallorders2009

    • Author(s)
      Akira Kaneko, Rina Nagahama
    • Journal Title

      Nat. Sci. Report Ochanomizu Univ

      Volume: 60-1 Pages: 31-44

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Critical exponent of blowup for heat equation with logarithmic nonlinearity on paraboloidal domain2009

    • Author(s)
      Akira KANEKO, Shie NISHIKAWA
    • Journal Title

      Nat.Sci.Report Ochanomizu Univ 60

      Pages: 1-13

    • NAID

      120001868967

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Enumeration of switching graphs of small orders2009

    • Author(s)
      Akira KANEKO, Rina NAGAHAMA
    • Journal Title

      Nat.Sci.Report Ochanomizu Univ. 60

      Pages: 31-44

    • NAID

      120001868968

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Critical exponent of blowup for heat equation with logarithmic nonlinearity on Paraboloidal domain2009

    • Author(s)
      Akira Kaneko, Shie Nishikawa
    • Journal Title

      Nat.Sci.Report Ochanomizu Univ. 60

      Pages: 1-13

    • NAID

      120001868967

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Enumeration of switching graphs of small orders2009

    • Author(s)
      Akira Kaneko, Rina Nagahama
    • Journal Title

      Nat.Sci.Report Ochanomizu Univ. 60

      Pages: 31-44

    • NAID

      120001868968

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Identification of the Shape of Curvilinear Charge Distribution

    • Author(s)
      Akira KANEKO, Toshiko Kaneshige
    • Journal Title

      Technical Report OCHA-IS

      Volume: 10-1 Pages: 1-5

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Journal Article] SecondCritical Exponent of Blowup for Heat Equationwith Power-Logarithm Nonlinearity on Paraboloidally Perturbed Conical Domain

    • Author(s)
      Akira Kaneko, Shie Nishikawa
    • Journal Title

      Technical Report OCHA-IS

      Volume: 11-2 Pages: 1-6

    • Related Report
      2011 Final Research Report
  • [Presentation] 整数上の完全凖同型暗号の実装実験2012

    • Author(s)
      中村蓉子,粕川正充,金子晃
    • Organizer
      SCIS2012
    • Place of Presentation
      金沢エクセルホテル東急(石川県)
    • Year and Date
      2012-02-01
    • Related Report
      2011 Final Research Report
  • [Presentation] 整数上の完全準同型暗号の実装実験2012

    • Author(s)
      中村蓉子, 粕川正充, 金子晃
    • Organizer
      SCIS2012
    • Place of Presentation
      金沢エクセルホテル東急(石川県)
    • Year and Date
      2012-02-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] 空間曲線の曲率のオンライン筆跡鑑定への応用2012

    • Author(s)
      柴田絢子,粕川正充,金子晃
    • Organizer
      SCIS2012
    • Place of Presentation
      金沢エクセルホテル東急(石川県)
    • Year and Date
      2012-01-30
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Ubuntu Linuxでの気象庁Nhmのメイクと六甲おろしのシミュレーション2011

    • Author(s)
      余田史絵,金子晃
    • Organizer
      第13回非静力学モデルに関するワークショップ
    • Place of Presentation
      長岡技科大学(新潟県)
    • Year and Date
      2011-10-14
    • Related Report
      2011 Final Research Report
  • [Presentation] Ubuntu Linux での気象庁Nhmのメイクと六甲おろしのシミュレーション2011

    • Author(s)
      余田史絵, 金子晃
    • Organizer
      弟13回非静力学モデルに関するワークショップ
    • Place of Presentation
      長岡技科大学(新潟県)
    • Year and Date
      2011-10-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] NP問題と概零知識証明2010

    • Author(s)
      内藤章子,金子晃
    • Organizer
      SCIS2010
    • Place of Presentation
      香川県高松市サンポート
    • Year and Date
      2010-01-20
    • Related Report
      2011 Final Research Report
  • [Presentation] 口唇の動きを利用した顔画像による顔認証システム2010

    • Author(s)
      玉田竜子,金子晃
    • Organizer
      SCIS2010
    • Place of Presentation
      香川県高松市サンポート
    • Year and Date
      2010-01-19
    • Related Report
      2011 Final Research Report
  • [Presentation] 曲線状電荷分布の同定問題2009

    • Author(s)
      兼重利子、金子晃
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      大阪大学(一般講演)
    • Year and Date
      2009-09-28
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 曲線状電荷分布の同定問題2009

    • Author(s)
      兼重利子
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] 対数型非線型項を持つ非線型熱方程式の一般化された爆発の臨界指数の決定2009

    • Author(s)
      金子晃,西川史恵
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学(大阪府)
    • Year and Date
      2009-09-27
    • Related Report
      2011 Final Research Report
  • [Presentation] 対数型非線型項を持つ非線型熱方程式の一般化された爆発の臨界指数の決定2009

    • Author(s)
      金子晃, 西川史恵
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学(一般講演)
    • Year and Date
      2009-09-27
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Critical exponent for heat equation with logarithmic nonlinearity on paraboloidal domain2008

    • Author(s)
      西川史恵、金子晃
    • Organizer
      弟34回発展方程式研究会
    • Place of Presentation
      中央大学春日キャンパス(1時間講演)
    • Year and Date
      2008-12-18
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Critical Exponent for Heat Equation with Logarithmic Nonlinearity on Paraboloidal Domain2008

    • Author(s)
      西川史恵, 金子晃
    • Organizer
      弟34回発展方程式研究会
    • Place of Presentation
      中央大学春日キャンパス
    • Year and Date
      2008-12-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] 二方向投影トモグラフィの再構成解集合とグラフ2008

    • Author(s)
      長濱里奈, 金子晃
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      東京大学柏キャンパス
    • Year and Date
      2008-09-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] 2方向投影トモグラフィの解集合とグラフ2008

    • Author(s)
      長濱里奈、金子晃
    • Organizer
      日本応用数理学会年会
    • Place of Presentation
      東京大学柏キャンパス(一般講演)
    • Related Report
      2010 Self-evaluation Report
  • [Book] 数値計算講義2009

    • Author(s)
      金子晃
    • Total Pages
      260
    • Publisher
      サイエンス社
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Remarks]

    • URL

      http://www.kanenko.com/~kanenko/Preprint/pblist.html

    • Related Report
      2011 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi