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Differential equations reduced to transcendental equations including complete elliptic integrals and their global solution structure

Research Project

Project/Area Number 21540232
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionRyukoku University

Principal Investigator

YOTSUTANI Shoji  龍谷大学, 理工学部, 教授 (60128361)

Co-Investigator(Kenkyū-buntansha) MORITA Yoshihisa  龍谷大学, 理工学部, 教授 (10192783)
MATSUMOTO Waichiro  龍谷大学, 理工学部, 教授 (40093314)
NINOMIYA Hirokazu  明治大学, 理工学部, 教授 (90251610)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords非線形境界値問題 / 完全楕円積分 / 楕円関数 / 超越方程式 / 反応拡散方程式 / 線形化固有値問題 / Sturm-Liouville理論 / 非局所
Research Abstract

We have been developed the original method for differential equations. We obtain all exact solutions and derive transcendental equations equivalent to the global bifurcation structure of the given differential equations. We have developed this method and applied it various problems. Especially, as for a cross-diffusion equation in 1 dimensional case, we have discovered various devises to analyze transcendental equations, and obtained the method to show the global bifurcation structure. Furthermore, we have started to investigate the stability of stationary solutions including multidimensional case. We have also reveal the blowup phenomena of curvature for plane elastic closed curves and the global structure of all curves.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (49 results)

All 2012 2011 2010 2009 Other

All Journal Article (17 results) (of which Peer Reviewed: 17 results) Presentation (25 results) Book (3 results) Remarks (4 results)

  • [Journal Article] Spectrum comparison for a conserved reaction-diffusion system with a variational property2012

    • Author(s)
      Yoshihisa Morita
    • Journal Title

      Applied Analysis and Computation

      Volume: 1 Pages: 57-71

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global bifurcation structure on a shadow system with a source term-Representation of all solutions-2011

    • Author(s)
      H. Takaichi I. Takagi and S. Yotsutani
    • Journal Title

      Discrete and Continuous Dynamical Systems Supplement

      Pages: 1344-1350

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fast reaction limit of a three-component reaction-diffusion system2011

    • Author(s)
      H. Murakawa and H. Ninomiya
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 379 Pages: 150-170

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stacked Fronts for Cooperative Systems with Equal Diffusion Coefficients2011

    • Author(s)
      M. Iida, R. Lui, and H. Ninomiya
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 43 Pages: 1369-1389

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global bifurcation structure on a shadow system with a source term, Representation of all solutions2011

    • Author(s)
      H.Takaichi, I.Takagi, S.Yotsutani
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: Supplement Pages: 1344-1350

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fast reaction limit of a three-component reaction-diffusion system2011

    • Author(s)
      H.Murakawa, H.Ninomiya
    • Journal Title

      Journal of Mathematical Analysis and Application

      Volume: 379 Pages: 150-170

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic profiles of eigenfunctions for some 1-dimensional linearized eigenvalue problems2010

    • Author(s)
      T. Wakasa and S. Yotsutani
    • Journal Title

      Communication on Pure and Applied Analysis

      Volume: 9 Pages: 539-56

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Traveling wave solutions and entire solutions to reaction-diffusione quations2010

    • Author(s)
      Y. Morita and H. Ninomiya
    • Journal Title

      Sugaku Expositions

      Volume: 23 Pages: 213-233

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability and bifurcation of nonconstant solutions to a reaction-diffusion system with conservation of a mass2010

    • Author(s)
      Y. Morita and T. Ogawa
    • Journal Title

      Nonlinearity

      Volume: 23 Pages: 1387-1411

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of stabilized propagating wave segments in wave front interaction model2010

    • Author(s)
      J. S. Guo, H. Ninomiya and J. C. Tsai
    • Journal Title

      Physica D : Nonlinear Phenomena

      Volume: 239 Pages: 230-239

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic profiles of eigenfunctions for some 1-dimensional linearized eigenvalue problems2010

    • Author(s)
      T.Wakasa, S.Yotsutani
    • Journal Title

      Communication on Pure and Applied Analysis

      Volume: 9 Pages: 539-561

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Traveling wave solutions and entire solutions to reaction-diffusion equations2010

    • Author(s)
      Y.Morita, H.Ninomiya
    • Journal Title

      Sugaku Expositions

      Volume: 23 Pages: 213-233

    • NAID

      130004558838

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic profiles of eigenfunctions for some l-dimensional linearized eigenvalue problems2010

    • Author(s)
      T.Wakasa, S.Yotsutani
    • Journal Title

      Communication on Pure and AppliedAnalysis 9

      Pages: 539-561

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of stabilized propagating wave segments in wave front interaction model2010

    • Author(s)
      J.-S.Guo, H.Ninomiya, J.-C.Tsai
    • Journal Title

      Physica D : Nonlinear Phenomena 239

      Pages: 230-239

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] One can hear the shape of some non-convex drums, More Progress in Analysis2009

    • Author(s)
      W. Matsumoto, M. Murai and S. Yotsutani
    • Journal Title

      Proc. 5th ISAAC Congress

      Volume: 2009 Pages: 863-872

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] An entire solution to the Lotka-Volterra competition. diffusion equations2009

    • Author(s)
      Y. Morita and K. Tachibana
    • Volume
      40
    • Pages
      2217-2240
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] An entire solution to the Lotka-Volterra competition-diffusion equations2009

    • Author(s)
      Y.Morita, K.Tachibana
    • Journal Title

      SIAM J.Math.Anal. 40

      Pages: 2217-2240

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 微分方程式の解の極限形状と大域的分岐構造-弾性曲線・交差拡散方程式系を例として-2012

    • Author(s)
      四ツ谷晶二
    • Organizer
      2012年度日本数学会年会
    • Place of Presentation
      東京理科大学
    • Related Report
      2011 Final Research Report
  • [Presentation] 面積制約停留の平面閉弾性閉曲線の全体像と爆発現象2012

    • Author(s)
      村井・松本・四ツ谷
    • Organizer
      2012年度日本数学会年会,函数方程式分科会
    • Place of Presentation
      東京理科大学
    • Related Report
      2011 Final Research Report
  • [Presentation] Blow up phenomena for plane closed elastic curves and global structure2012

    • Author(s)
      Shoji Yotsutani
    • Place of Presentation
      九州大学西新プラザ
    • Related Report
      2011 Final Research Report
  • [Presentation] Blow up phenomena for plane closed elastic curves2012

    • Author(s)
      Shoji Yotsutani
    • Organizer
      The 20th Workshop on Differential Equations and Its Applications
    • Place of Presentation
      Tamkang University, Taiwan
    • Related Report
      2011 Final Research Report
  • [Presentation] 微分方程式の解の極限形状と大域的分岐構造-弾性曲線・交差拡散方程式系を例として-2011

    • Author(s)
      四ツ谷晶二
    • Organizer
      日本数学会年会企画特別講演
    • Place of Presentation
      東京理科大学神楽坂学舎(東京都)(招待講演)
    • Year and Date
      2011-03-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] 平面弾性閉曲線における曲率の爆発現象2011

    • Author(s)
      村井・松本・四ツ谷
    • Organizer
      2011年度日本数学会秋季総合分科会,函数方程式分科会
    • Place of Presentation
      信州大学
    • Related Report
      2011 Final Research Report
  • [Presentation] A limiting system in the Lotka-Volterra competition with cross-diffusion2011

    • Author(s)
      Shoji Yotsutani
    • Organizer
      The workshop is in mathematical ecology
    • Place of Presentation
      East China Normal University, China
    • Related Report
      2011 Final Research Report
  • [Presentation] 回転数1の平面弾性閉曲線における曲率の爆発現象2011

    • Author(s)
      三好・村井・松本・四ツ谷
    • Organizer
      2011年度日本数学会年会,函数方程式分科会
    • Place of Presentation
      アブストラクト,早稲田大学
    • Related Report
      2011 Final Research Report
  • [Presentation] Lotka-Volterra competition with cross-diffusion2011

    • Author(s)
      Shoji Yotsutani
    • Organizer
      The 19th Workshop on Differential Equations and Its Applications
    • Place of Presentation
      National Cheng Kung Univsity, Taiwan
    • Related Report
      2011 Final Research Report
  • [Presentation] Multiplicity of solutions to a limiting system in the Lotka-Volterra competition with cross-diffusion2011

    • Author(s)
      Shoji Yotsutani
    • Organizer
      The 19th Workshop on Differential Equations and Its Applications
    • Place of Presentation
      National Cheng Kung Univsity, Taiwan(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] A limiting system in the Lotka-Volterra competition with cross-diffusion2011

    • Author(s)
      Shoji Yotsutani
    • Organizer
      The workshop is in mathematical ecology, (9Omin.x 4)
    • Place of Presentation
      East China Normal University, China(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] 完全楕円積分の商の評価式とその応用2010

    • Author(s)
      村井・松本・四ツ谷
    • Organizer
      日本数学会・2010年度年会
    • Place of Presentation
      慶応大学理工学部
    • Year and Date
      2010-03-24
    • Related Report
      2011 Final Research Report
  • [Presentation] 定常解の大域的分岐構造解析と完全楕円積分の高精度近似2010

    • Author(s)
      四ツ谷晶二
    • Organizer
      研究集会「HMAセミナー・冬の研究会2010」
    • Place of Presentation
      広島大学総合科学部
    • Year and Date
      2010-01-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Blow up phenomena in closed plane elastic curves2010

    • Author(s)
      Shoji Yotsutani
    • Organizer
      Nonlinear Analysis and Integrable Systems
    • Place of Presentation
      Ryukoku Univ., Japan
    • Related Report
      2011 Final Research Report
  • [Presentation] Multiplicity of solutions to a limiting system in the Lotka-Volterra competition with cross-diffusion2010

    • Author(s)
      Shoji Yotsutani
    • Place of Presentation
      RIMS, Kyoto Univ. Japan
    • Related Report
      2011 Final Research Report
  • [Presentation] 平面弾性閉曲線における曲率の爆発現象2010

    • Author(s)
      三好・村井・松本・四ツ谷
    • Organizer
      2010年度日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Related Report
      2011 Final Research Report
  • [Presentation] On a shadow system to the Gierer-Meinhart system with a non-local term2010

    • Author(s)
      S. Yotsutani
    • Organizer
      8-th AIMS conferenceon Dynamical systems, Differential equations and Applications, Special Session 31
    • Place of Presentation
      Dresden Univ. of Tech., Dresden, Germany
    • Related Report
      2011 Final Research Report
  • [Presentation] On a shadow system to the Gierer-Meinhart system with a non-local term2010

    • Author(s)
      S.Yotsutani
    • Organizer
      The 8th AIMS Conference on Dynamical Systems
    • Place of Presentation
      Dresden Univ.of Tech., Dresden, German
    • Related Report
      2010 Annual Research Report
  • [Presentation] Cahn-Hilliard方程式の定常解の大域的分岐構造と関連する話題2009

    • Author(s)
      四ツ谷晶二
    • Organizer
      研究集会「偏微分方程式と現象:PDEs and Phenomena in Miyazaki 2009」
    • Place of Presentation
      宮崎大学工学部
    • Year and Date
      2009-11-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Cahn-Hilliard方程式の定常解の大域的分岐構造と関連する話題2009

    • Author(s)
      四ツ谷晶二
    • Organizer
      研究集会「夏の偏微方程式セミナー2009」
    • Place of Presentation
      龍谷大学ともいき荘
    • Year and Date
      2009-08-28
    • Related Report
      2011 Final Research Report
  • [Presentation] 数式処理の微分方程式研究への応用2009

    • Author(s)
      四ツ谷晶二
    • Organizer
      RIMS研究集会「数式処理と教育」
    • Place of Presentation
      京大会館
    • Year and Date
      2009-08-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Asymptotic profiles of eigenfunctions for some l-dimensional linearized eigenvalue problems2009

    • Author(s)
      S.Yotsutani
    • Organizer
      The Second International Conference on Reaction-Diffusion Systems and Viscosity Solutions
    • Place of Presentation
      Providence University, Taiwan
    • Year and Date
      2009-07-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] Asymptotic profiles of eigenfunctions for some 1-dimensional linearized eigenvalue problems2009

    • Author(s)
      S. Yotsutani
    • Organizer
      The Second International Conference on Reaction-Diffusion Systems and Viscosity Solutions
    • Place of Presentation
      Providence University, Taiwan
    • Year and Date
      2009-07-15
    • Related Report
      2011 Final Research Report
  • [Presentation] 面積制約条件付の閉平面弾性曲線と関連する話題2009

    • Author(s)
      四ツ谷晶二
    • Organizer
      RIMS研究集会「保存則と幾何学的偏微分方程式とその応用」
    • Place of Presentation
      京大会館
    • Year and Date
      2009-06-10
    • Related Report
      2011 Final Research Report
  • [Presentation] 面積を規定した2次元弾性曲線の全体像2009

    • Author(s)
      四ツ谷晶二
    • Organizer
      第2回RDSセミナー
    • Place of Presentation
      明治大学生田キャンパス
    • Year and Date
      2009-05-19
    • Related Report
      2011 Final Research Report
  • [Book] 生物リズムと力学系2011

    • Author(s)
      郡宏, 森田善久
    • Total Pages
      192
    • Publisher
      共立出版
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Book] 岩波数学叢書「ギンツブルク-ランダウ方程式と安定性解析」2009

    • Author(s)
      神保秀一・森田善久
    • Total Pages
      326
    • Publisher
      岩波書店
    • Related Report
      2011 Final Research Report
  • [Book] 岩波数学叢書「ギンツブルクーランダウ方程式と安定性解析」2009

    • Author(s)
      神保秀一・森田善久
    • Total Pages
      326
    • Publisher
      岩波書店
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.ryukoku.ac.jp/who/detail/592188/

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.ryukoku.ac.jp/who/detail/592188/

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.ryukoku.ac.jp/who/detail/592188/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.ryukoku.ac.jp/who/detail/592188/

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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