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2005 Fiscal Year Final Research Report Summary

Global solution structure and the stability of nonlocal nonlinear second order boundary value problems with definite integrals

Research Project

Project/Area Number 15540220
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  Ryukoku Univ., Faculty of Sci. and Tech., Professor, 理工学部, 教授 (60128361)

Co-Investigator(Kenkyū-buntansha) MORITA Yoshihisa  Ryukoku Univ., Faculty of Sci. and Tech., Professor, 理工学部, 教授 (10192783)
MATSUMOTO Waichiro  Ryukoku Univ., Faculty of Sci. and Tech., Professor, 理工学部, 教授 (40093314)
OKA Hiroe (國府 宏枝)  Ryukoku Univ., Faculty of Sci. and Tech., Professor, 理工学部, 教授 (20215221)
NINOMIYA Hirokazu  Ryukoku Univ., Faculty of Sci. and Tech., Ass.Professor, 理工学部, 助教授 (90251610)
YANAGIDA Eiji  Tohoku Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80174548)
Project Period (FY) 2003 – 2005
Keywordscross-diffusion / nonlinear elliptic equation / nonlocal / nonlinear boundary value problem / periodic boundary condition / Ginzburg-Landau equation / positive radial solution / singular solution
Research Abstract

First, Lou-Ni-Yotsutani [DCDS 2004] investigated a limiting equation to a cross-diffusion equation that appears in mathematical biology. We showed that it has different kinds of singular solutions and revealed the structure of all solutions.
This problem is a nonlocal nonlinear elliptic boundary problem, for which no method was known to solve it. We discovered a new method, which are the combination of the modern method of PDE and classical analysis and algebra.
There are a lot of interesting problems for which our method is applicable.
A problem of the Oseen's spiral flow is one of them, for which we obtained the complete bifurcation diagram in Ikeda-Kondo-Okamoto-Yotsutani [CPAA 2003].
Matsumoto-Murai-Yotsutani [Pisa, 2005] gave the complete answer for a problem to determine curves with the least energy under the given length.
Second, Kosugi-Morita-Yotsutani [CPAA 2005, J.Math.Phy. 2005] have revealed the complete Global bifurcation branches one dimensional Ginzburg-Landau equations with periodic boundary conditions.

  • Research Products

    (14 results)

All 2005 2004 2003

All Journal Article (13 results) Book (1 results)

  • [Journal Article] A complete bifurcation diagram of the Ginzburg-Landau equation with periodic boundary conditions2005

    • Author(s)
      S.Kosugi, Y.Morita, S.Yotsutani
    • Journal Title

      Communication on Pure and Applied Analysis 4・3

      Pages: 665-682

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Global bifurcation structure of a one dimensional Ginzburg-Landau model2005

    • Author(s)
      S.Kosugi, Y.Morita, S.Yotsutani
    • Journal Title

      J. Math. Phys. 46・095111

      Pages: 1-24

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Structure of positive radial solutions including singular solutions to Matukuma's equation2005

    • Author(s)
      H.Morishita, E.Yanagida, S.Yotsutani
    • Journal Title

      Communication on Pure and Applied Analysis 4・4

      Pages: 871-888

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A complete bifurcation diagram of the Ginzburg-Landau equation with periodic boundary conditions2005

    • Author(s)
      S.Kosugi, Y.Morita, S.Yotsutani
    • Journal Title

      Comm.on Pure and Appl.Anal. 4・3

      Pages: 665-682

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Global bifurcation structure of a one dimensional Ginzburg-Landau model2005

    • Author(s)
      S.Kosugi, Y.Morita, S.Yotsutani
    • Journal Title

      J.Math.Phys. 46・095111

      Pages: 1-24

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Structure of positive radial solutions including singular solutions to Matukuma' s equation2005

    • Author(s)
      H.Morishita, E.Yanagida, S.Yotsutani
    • Journal Title

      Comm.on Pure and Appl.Anal. 4・4

      Pages: 871-888

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Phase Space Analysis of Partial Differential Equations II2005

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

      CENTRO DE RICERCA MATEMATIC ENNIO DE GIORGI, SCUOLA NORMALE SUPERIORE PISA

      Pages: 341-361

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On a Limiting System in the Lotka-Volterra Competition with Cross-Diffusion2004

    • Author(s)
      Y.Lou, W.-M.Ni, S.Yotsutani
    • Journal Title

      Discrete and Continuous Dynamical Systems 10・1

      Pages: 435-458

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On a limiting system in the Lotka-Volterra competition with cross-diffusion2004

    • Author(s)
      Y.Lou, W.-M.Ni, S.Yotsutani
    • Journal Title

      Discrete and Cont.Dynam.Sys. 10・1

      Pages: 435-453

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows2003

    • Author(s)
      H.Ikeda, K.Kondo, H.Okamoto, S.Yotsutani
    • Journal Title

      Communication on Pure and Applied Analysis 3・3

      Pages: 381-390

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Recent Topics on Nonlinear Partial Differential Equations : Structure of Radial Solutions for Semilinear Elliptic Equations2003

    • Author(s)
      E.Yanagida, S.Yotsutani
    • Journal Title

      Amer. Math. Soc. Transl., Series : Selected Papers on Analysis and Differential Equations 2・211

      Pages: 121-137

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen' s spiral flows2003

    • Author(s)
      H.Ikeda, K.Kondo, H.Okamoto, S.Yotsutani
    • Journal Title

      Comm.on Pure and Appl.Anal. 3・3

      Pages: 381-390

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Recent topics on nonlinear partial differential equations : Selected Papers on Analysis and Differential Equations2003

    • Author(s)
      E.Yanagida, S.Yotsutani
    • Journal Title

      Amer.Math.Soc.Transl.Series. 2・211

      Pages: 121-137

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] Phase Space Analysis of Partial Differential Equations II2005

    • Author(s)
      W.Matsumoto, M.Murai, S.Yotsutani
    • Total Pages
      345-361
    • Publisher
      CENTRO DE RICERCA MATEMATICA ENNIO DE GIORGI, SCUOLA NORMALE SUPERIORE PISA
    • Description
      「研究成果報告書概要(和文)」より

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Published: 2007-12-13  

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