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Study on the nonlinear phenomena with moving boundaries

Research Project

Project/Area Number 16540184
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

ISHIMURA Naoyuki  Hitotsubashi University, Graduate School of Enocomics, Professor, 大学院経済学研究科, 教授 (80212934)

Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsphase separation / nonlinear PDE / EOM system / Mathematical Finance / transaction costs / 相分離現象 / EOM系モデル / 分岐現象 / 特異極限 / 遷移層方程式 / 定常解の構造 / 変分法
Research Abstract

This research project is mainly concerned with the next two subjects, among the popular research topics of nonlinear phenomena involving the moving boundaries. 1 : Study on the phase separation. 2 : Study on the exercise boundary in mathematical finances.
1.The author has been tackling the analysis of a model equation proposed by Professor T.Eguchi, which describes the phase separation in terms of two unknown variables. One is the local concentration and the other is the local degree of order. The model consists of coupled two evolution equations ; one is 4^<th> order and hence the analysis is tough. We concentrate on the one-dimensional case and we obtain fairy a lot of results. The first one is one the existence of solutions and the structure of steady state solutions. Analysis of a singular perturbation problem and a bifurcation problem then follows. We publish these papers in various journal, which are rather well estimated by anonymous referees.
2.The author gives a set of exact solutions for the model equation proposed by K.Takaoka, which extends the famous Black-Scholes analysis. Then the author tries to solve the partial differential equations with the effect of transaction costs. The paper is submitted now.
The research of the phase separation still continues. The direction with respect to the dynamical system seems promising and the work is now in progress.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (26 results)

All 2007 2006 2005 2004

All Journal Article (24 results) Book (2 results)

  • [Journal Article] Primary University Notes2007

    • Author(s)
      T.Fujita, N.Ishimura, A.Fujioka
    • Journal Title

      Basic Calculus(Jikkyo syuppan)

      Pages: 104-104

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Primary University Notes2007

    • Author(s)
      T.Fujita, N.Ishimura, A.Fujioka
    • Journal Title

      Basic Linear Algebra(Jikkyo syuppan)

      Pages: 95-95

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Bifurcations of steady state for the Eguchi-Oki-Matsumura model of phase separation2006

    • Author(s)
      Naoyuki ISHIMURA et al.
    • Journal Title

      Applicable Analysis 85

      Pages: 831-843

    • NAID

      120006933453

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Exact solutions of a model for asset prices by K. Takaoka2006

    • Author(s)
      Naoyuki ISHIMURA et al.
    • Journal Title

      Asia-Pacific Financial Markets 11

      Pages: 445-451

    • NAID

      120000814904

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Bifurcations of steady state for the Eguchi-Oki Matsumura model of phase separation2006

    • Author(s)
      N.Ishimura, K.-I.Nakamura, M.A.Nakamura
    • Journal Title

      Applicable Analysis 85

      Pages: 831-843

    • NAID

      120006933453

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Exact solutions of a model for asset prices by K. Takaoka2006

    • Author(s)
      N.Ishimura, T.-H Sakaguchi
    • Journal Title

      Asia-Pacific Financial Markets 11

      Pages: 445-451

    • NAID

      120000814904

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Bifurcation of steady states for the Eguchi-Oki-Matsumura model of phase separation2006

    • Author(s)
      Naoyuki ISHIMURA, Ken-Ichi NAKAMURA, MasaAki NAKAMURA
    • Journal Title

      Applicable Analysis 85・6-7

      Pages: 831-843

    • NAID

      120006933453

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Exact solutions of a model for asset prices by K.Takaoka2006

    • Author(s)
      Naoyuki ISHIMURA, Toshi-Hiko SAKAGUCHI
    • Journal Title

      Asia-Pacific Financial Markets 11・4

      Pages: 445-451

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Singular perturbation problem for steady state solutions to a model equation of phase separation2005

    • Author(s)
      Takao HANADA et al.
    • Journal Title

      Zeitshrift fur Angewandte Mathematik and Mechanik 85

      Pages: 896-903

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Singular perturbation problem for steady state solutions to a model equation of phase separation2005

    • Author(s)
      T.Hanada, N.Ishimura, M.A.Nakamura
    • Journal Title

      Zeitshrift fur Angewandte Mathematik and Mechanik 85

      Pages: 896-903

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Singular perturbation problem for steady state solutions to a model equation of phase separation2005

    • Author(s)
      Takao HANADA, Naoyuki ISHIMURA, Masaaki NAKAMURA
    • Journal Title

      Zeitshrift Angewandte Mathematik und Mechanik (ZAMM) 85巻・12号

      Pages: 896-903

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On the Eguchi-Oki-Matsumura equation for phase separation in one space dimension2005

    • Author(s)
      Naoyuki ISHIMURA, Takao HANADA, MasaAki NAKAMURA
    • Journal Title

      SIAM Journal on Mathematical Analysis 36

      Pages: 463-478

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the Eguchi-Oki-Matsumura equation for phase separation in one space dimension2004

    • Author(s)
      Takao HANADA et al.
    • Journal Title

      SIAM Journal on Mathematical Analysis 36

      Pages: 463-478

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stable finite difference scheme for a model equation of phase separation2004

    • Author(s)
      Takao HANADA et al.
    • Journal Title

      Applied Mathematics and Computation 151

      Pages: 95-104

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An elementary approach to the analysis of exact solutions for the Navier-Stokes stagnation flows with slips2004

    • Author(s)
      Naoyuki ISHIMURA et al.
    • Journal Title

      Archive der Mathematik 82

      Pages: 432-441

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Self-similar solutions for the kinematic model equation of spiral waves2004

    • Author(s)
      Jong-Shenq GUO et al.
    • Journal Title

      Physica D 198

      Pages: 197-211

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] One-phase Stefan problems for sublinear heat equations : Asymptotic behavior of solutions2004

    • Author(s)
      Toyohiko AIKI et al.
    • Journal Title

      Communications in Applied Analysis 8

      Pages: 1-15

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On the Eguchi-Oki-Matsumura equation for phase separation in one space dimension2004

    • Author(s)
      T.Hanada, N.Ishimura, M.A.Nakamura
    • Journal Title

      SIAM Journal on Mathematical Analysis 36

      Pages: 463-478

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stable finite difference scheme for a model equation of phase separation2004

    • Author(s)
      T.Hanada, N.Ishimura, M.A.Nakamura
    • Journal Title

      A.pplied Mathematics and Computation 151

      Pages: 95-104

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An elementary approach to the analysis of exact solutions for the Navier-Stokes stagnation flows with slips2004

    • Author(s)
      N.Ishimura, T.K.Ushijima
    • Journal Title

      Archive der Mathematik 82

      Pages: 432-441

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Self-similar solutions for the kinematic model equation of spiral waves2004

    • Author(s)
      J.-S.Guo, N.Ishimura, C.-C.Wu
    • Journal Title

      Physica D 198

      Pages: 197-211

    • NAID

      120000815950

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] One-phase Stefan problems for sublinear heat equations : Asymptotic behavior of solutions2004

    • Author(s)
      T.Aiki, H.Imai, N.Ishimura, Y.Yamada
    • Journal Title

      Communications in Applied Analysis 8

      Pages: 1-15

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An elementary approach to the analysis of exact solutions for the Navier-Stokes stagnation flows with slips2004

    • Author(s)
      Naoyuki ISHIMURA, TaKeo K., USHIJIMRA
    • Journal Title

      Archive der Mathematik 82

      Pages: 432-441

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Self-similar solutions for the kinematic model equation of spiral waves2004

    • Author(s)
      Naoyuki ISHIMURA, Jong-Shenq GUO, Chin-Chin WU
    • Journal Title

      Physica D 198

      Pages: 197-211

    • NAID

      120000815950

    • Related Report
      2004 Annual Research Report
  • [Book] Primary 大学ノート 微分積分2007

    • Author(s)
      藤田岳彦 他
    • Total Pages
      104
    • Publisher
      実教出版
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Book] Primary 大学ノート 線形代数2007

    • Author(s)
      藤田岳彦 他
    • Total Pages
      95
    • Publisher
      実教出版
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary

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Published: 2004-04-01   Modified: 2016-04-21  

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