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2004 Fiscal Year Final Research Report Summary

Research on the structure and stability of the dynamical system describing phase transition phenomena

Research Project

Project/Area Number 13440052
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

KENMOCHI Nobuyuki  Chiba University, Faculty of Education, Professor, 教育学部, 教授 (00033887)

Co-Investigator(Kenkyū-buntansha) KURANO Masami  Chiba University, Faculty of Education, Professor, 教育学部, 教授 (70029487)
KOSHIKAWA Hiroaki  Chiba University, Faculty of Education, Professor, 教育学部, 教授 (60000866)
OTANI Mitsuharu  Waseda Univ., School of Science & Technology, Professor, 理工学術院, 教授 (30119656)
AIKI Toyohiko  Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (90231745)
ITO Akio  Kinki University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30303506)
Project Period (FY) 2001 – 2004
Keywordsphase transition / stability of dynamical system / Stefan problem / global attractor / subdifferential / nonlinear evolution equation
Research Abstract

The subjects of this project are the following :
(1)Modelings of phase transition phenomena with their mathematical theory
(2)Formulations of the related optimal control problems and numerical simulations
(3)Return of the research results to the school education
Concerning (1), on the basis of the fundamental laws of the thermo-mechanics, we investigated the structure (phase change, component separation, damage evolution, ordering of atoms) of materials from the view-point of the theory of dymanical systems. Especially, during the last two years (2003-2004) of the project, we treated a class of models for irreversible phase change phenomena, taking account of the process of damage, and evolved its mathematical theory. In our research the subdifferential theory, which have been accumulated for these 15 years, worked very well and we had a big progress more than we expected. Concerning (2), proposing some formulations of optimal control problems in which control parameters are described by a class of hysteresis functions, we finished almost the theoretical part of the problems and tried partially their numerical tests. It was pointed out that there are still some questions which should be improved. Many papers treating subjects (1)and (2)were published and we organized two international conferences during this research project.
As far as (3)is concerned, many practices were reported in the meetings "Mathematical analysis of phase transitions and their related mathematics education" which we organized every year. We paid our attention to time-dependent phenomena noticed easily in our daily lives, verifying very carefully their value-added educational aspects as teaching materials of mathematics or sciences for the secondary school. We expect that this research enables to provide new teaching materials by which students can perceive usefulness of mathematics.

  • Research Products

    (14 results)

All 2004 2003 2002 2001

All Journal Article (12 results) Book (2 results)

  • [Journal Article] A new class of doubly nonlinear evolution equations2004

    • Author(s)
      阿曽雅泰, 深尾武史, 剣持信幸
    • Journal Title

      Taiwanese Journal of Mathematics 8

      Pages: 103-124

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A new class of doubly nonlinear evolution equations2004

    • Author(s)
      M.Aso, T.Fukao, N.Kenmochi
    • Journal Title

      Taiwanese Journal of Mathematics Vol.8

      Pages: 103-124

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Mathematical treatment of phase separation with order-disorder structure in binary mixtures2003

    • Author(s)
      伊藤昭夫, 剣持信幸, M.Niezgodka
    • Journal Title

      Advances in Mathematical Sciences and Applications 13

      Pages: 357-385

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Stability for a phase field model with the total variation functional as the interfacial energy2003

    • Author(s)
      剣持 信幸, 白川 健
    • Journal Title

      Nonlinear Analysis 53

      Pages: 425-440

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Mathematical treatment of phase separation with order-disorder structure in binary mixtures2003

    • Author(s)
      A.Ito, N.Kenmochi, M.Niezgodka
    • Journal Title

      Advances in Mathematical Sciences and Applications Vol.13

      Pages: 357-385

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Stability for a phase field model with the total variation functional as the interfacial energy2003

    • Author(s)
      N.Kenmochi, K.Shirakawa
    • Journal Title

      Nonlinear Analysis Vol.53

      Pages: 425-440

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Phase-field systems with vectorial order parameters including diffusional hysteresis effects2002

    • Author(s)
      剣持 信幸, J.Sprekels
    • Journal Title

      Communications in Pure and Applied Analysis 1

      Pages: 495-511

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Ordinary differential systems describing hysteresis effects and numerical simulations2002

    • Author(s)
      E.Minchev, 岡崎貴宣, 剣持信幸
    • Journal Title

      Abstract and Applied Analysis 7

      Pages: 563-584

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Phase-field systems with vectorial order parameters including diffusional hysteresis effects2002

    • Author(s)
      N.Kenmochi, J.Sprekels
    • Journal Title

      Communications in Pure and Applied Analysis Vol.1

      Pages: 495-511

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Ordinary differential systems describing hysteresis effects and numerical simulations2002

    • Author(s)
      E.Minchev, T.Okazaki, N.Kenmochi
    • Journal Title

      Abstract and Applied Analysis Vol.7

      Pages: 563-584

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Stability for a parabolic variational inequality associated with total variation functional2001

    • Author(s)
      剣持 信幸, 白川 健
    • Journal Title

      Funkcialaj Ekvacioj 44

      Pages: 119-137

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Stability for a parabolic variational inequality associated with total variation functional2001

    • Author(s)
      N.Kenmochi, K.Shirakawa
    • Journal Title

      Funkcialaj Ekvacioj Vol.44

      Pages: 119-137

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] Nonlinear Partial Differential Equations and their Applications2004

    • Author(s)
      剣持信幸, 大谷光春, S.Zheng
    • Total Pages
      534
    • Publisher
      学校図書(株)
    • Description
      「研究成果報告書概要(和文)」より
  • [Book] Nonlinear Partial Differential Equations and their Applications(Mathematical Sciences and Applications, Vol.20)2004

    • Author(s)
      N.Kenmochi, M.Otani, S.Zheng
    • Total Pages
      534
    • Publisher
      Gakuto International Series
    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2006-07-11  

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