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Analysis of nonlinear phenomena describing hysteresis operators

Research Project

Project/Area Number 14540169
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

AIKI Toyohiko  Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (90231745)

Co-Investigator(Kenkyū-buntansha) YAMADA Masahiro  Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00263666)
SATO Naoki  Nagaoka College of Technology, Liberal Arts, Associate Professor, 一般教育科, 助教授 (90280370)
TAKEUCHI Shigeru  Gifu University, Faculty of Education, Professor, 教育学部, 教授 (30021330)
ITO Akio  Kinki University, Faculty of Engineering, Lecturer, 工学部, 講師 (30303506)
ISHIWATA Tetsuya  Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (50334917)
山崎 教昭  室蘭工業大学, 工学部, 講師 (90333658)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2003: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2002: ¥1,800,000 (Direct Cost: ¥1,800,000)
Keywordshysteresis operator / shape memory alloy / nonlinear PDE / ferromagnetic / weak solution of PDE / ヒステリシス / 非線形現象 / アトラククー / 力学系 / 発展方程式 / ステファン問題
Research Abstract

[Shape memory alloy problems] : In the dynamics of shape memory alloy materials the relationship between the strain and the stress can not be described by a usual function, and is represented by a hysteresis operator. Here, the main idea of this research project is to describe the relationship by using a general stop operator. Moreover, we consider the ordinary differential equation, which is equivalent to the generalized stop operator, and propose a system describing the dynamics of shape memory alloys. The system consists of partial differential equations and the ordinary differential equation and is studied in this project. We consider the one-dimensional problem, in which we dealt the ordinary differential equation without an approximation. In this case the regularity of a solution to the ordinary differential equation is not enough in space so that it is impossible to prove the existence of a classical solution. Then we showed the existence and the uniqueness of a weak solution. Also, we considered a shape memory alloy problem in three dimensions. In 3-d case the regularity of a solution is not good. Hence, we proved the well-posed ness for only approximated problem. Here, we note that we also have a plan to analyze our mathematical model, numerically. Now, we do not success to get a numerical solution of a complete problem and have an algorithm for solving a kinetic equation, which is most difficult to compute in our process.
[magnetization in ferromagnetic] : By using a generalized Duhem model we propose a mathematical model for dynamics of ferromagnetic and prove the well-posedness.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] AIKI, Toyohiko: "Uniqueness for multi-dimensional Stefan problems with nonlinear boundary conditions described by maximal monotone operators"Differential and Integral Equations. 15. 973-1008 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko, IMAI, Hitoshi, ISHIMURA Naoyuki: "Well-posedness of one-phase Stefan problems for sublinear heat equations"Journal of Nonlinear Analysis : Theory, Methods, and Applications. 51. 587-606 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko, KENMOCHI, Nobuyuki: "Models for shape memory alloys described by subdifferentials of indicator functions"Elliptic and Parabolic Problems, Rolduc and Gaeta 2001, World Scientific Publishing. 1-10 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko: "One-dimensional shape memory alloy problems including a hysteresis operator"Funkcialaj Ekvaccioj. 46. 441-469 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ishiwata, S.Yazaki: "On the blow-up rate for fast blow-up solutions arising in an anisotropic crystalline motion"Journal of Computational and Applied Mathematics. 159. 55-64 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko, IMAI, Hitoshi, ISHIMURA Naoyuki: "One-phase Stefan problems for sublinear heat equations : Asymptotic behavior of solutions"Communications in Applied Analysis. 8. 1-15 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Toyohiko Aiki: "Uniqueness for multi-dimensional Stefan problems with nonlinear boundary conditions described by maximal monotone operators."Differential and Integral Equations. 15. 973-1008 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko, IMAI, Hitoshi, ISHIMURA, Naoyuki: "Well-posedness of one-phase Stefan problems for sublinear heat equations."Journal of Nonlinear Analysis : Theory, Methods, and Applications. 51. 587-606 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko, KENMOCHI, Nobuyuki: "Models for shape memory alloys described by subdifferentials of indicator functions."Elliptic and Parabolic Problems, Rolduc and Gaeta 2001. 1-10 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko: "One-dimensional shape memory alloy problems including a hysteresis operator."Funkcialaj Ekvaccioj. 46. 441-469 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ishiwata, S.Yazaki: "On the blow-up rate for fast blow-up solutions arising in an anisotropic crystalline motion."Journal of Computational Applied and Mathematics. 159. 55-64 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko, IMAI, Hitoshi, ISHIMURA Naoyuki: "One-phase Stefan problems for sublinear heat equations : Asymptotic behavior of solutions."Communications in Applied Analysis. 8. 1-15 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] AIKI, Toyohiko: "Uniqueness for multi-dimensional Stefan problems with nonlinear boundary conditions described by maximal monotone operators"Differential and Integral Equations. 15. 973-1008 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] AIKI, Toyohiko, IMAI, Hitoshi, ISHIMURA Naoyuki: "Well-posedness of one-phase Stefan problems for sublinear heat equations"Journal of Nonlinear Analysis : Theory, Methods, and Applications. 51. 587-606 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] AIKI, Toyohiko, IMAI, Hitoshi, ISHIMURA, Naoyuki, YAMADA Yoshio: "One-phase Stefan problems for sublinear heat equations : Asymptotic behavior of solutions"Communications in Applied Analysis. 8. 1-15 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] AIKI, Toyohiko: "One-dimensional shape memory alloy problems including a hysteresis operator"Funkcialaj Ekvaccioj. 48. 441-469 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] YAMADA, Masahiro: "Inequalities on derivatives of harmonic Bergman functions"Scientiae Mathematicae Japonicae Online. 9. 111-118 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Ishiwata, S.Yazaki: "On the blow-up rate for fast blow-up solutions arising in an anisotropic crystalline motion"Journal of Computational and Applied Mathematics. 159. 55-64 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Aiki: "Uniqueness for multi-dimensional Stefan problems with nonlinear boundary conditions described by maximal monotone operators"Differential and Integral Equations. 15. 973-1008 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Aiki, H.Imai: "Well-posedness of one-phase Stefan problems for sublinear heat equations"Journal of Nonlinear Analysis. 51. 587-606 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Aiki, N.Kenmochi: "Models for shape memory alloys described by subdifferentials of indicator functions"Elliptic and Parabolic Problems, Rolduc and Gaeta 2001, World Scientific Publishing. 1-10 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Aiki: "One-dimensional shape memory alloy problems including a hysteresis operator"Funkcialaj Ekvaccioj. (掲載予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Gokieli, A.Ito: "Global attractor for the Cahn-Hilliard/Allen-Cahn system"Nonlinear Aanlysis. 52. 1821-1841 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] N.Yamazaki: "Attractors for non-autonomous multivalued evolution systems generated by time-dependent subdifferentials"Abstract and Applied Analysis. 7. 453-473 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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