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Mathematical Analysis for the Thermo-Elasto-Plasticity of Shape Memory Alloys

Research Project

Project/Area Number 22740097
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionEhime University (2011-2012)
Ube National College of Technology (2010)

Principal Investigator

YOSHIKAWA Shuji  愛媛大学, 大学院・理工学研究科, 准教授 (80435461)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords非線形偏微分方程式, / 熱弾性 / 塑性 / 相転移 / 形状記憶合金 / 非線形偏微分方程式
Research Abstract

Shape memory alloys system is one of thermo-elastic (thermo-visco-elasto-plastic) systems which describe the relation between displacement vector and temperature. We studied equations related to these topics. Our results for this research subject are as follows : (1) stability of steady state for multi-dimensional shape memory alloys system (2) smoothing effect and asymptotic profile of the solution for semilinear beam equation with weak damping, (3) asymptotic profiles of solutions for the Cahn-Hilliard equation with inertial term, (4) asymptotic profiles of solutions for the Falk-Konopka system of shape memory alloys with weak damping.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (24 results)

All 2013 2012 2011 2010 Other

All Journal Article (10 results) (of which Peer Reviewed: 5 results) Presentation (11 results) (of which Invited: 2 results) Remarks (3 results)

  • [Journal Article] On the initial value problem of the semilinear beam equation with weak damping I : smoothing effect2013

    • Author(s)
      Hiroshi Takeda, Shuji Yoshikawa
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 401 Pages: 244-258

    • Related Report
      2012 Final Research Report
  • [Journal Article] On the initial value problem of the semilinear beam equation with weak damping I: smoothing effect2013

    • Author(s)
      Hiroshi Takeda, Shuji Yoshikawa
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 401 Issue: 1 Pages: 244-258

    • DOI

      10.1016/j.jmaa.2012.12.015

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the initial value problem of the semilinear beam equation with weak damping II : asymptotic profiles2012

    • Author(s)
      Hiroshi Takeda, Shuji Yoshikawa
    • Journal Title

      Journal of Differential Equations

      Volume: 253 Pages: 3061-3080

    • Related Report
      2012 Final Research Report
  • [Journal Article] Asymptotic profile of solutions for the limit unstable Cahn-Hilliard equation with inertial term2012

    • Author(s)
      Hiroshi Takeda, Shuji Yoshikawa
    • Journal Title

      Differential and Integral Equations

      Volume: 25 Pages: 341-362

    • Related Report
      2012 Final Research Report
  • [Journal Article] Stability of the steady state for multi-dimensional thermoelastic systems of shape memory alloys2012

    • Author(s)
      Takashi Suzuki, Shuji Yoshikawa
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series S

      Volume: 5 Pages: 209-217

    • Related Report
      2012 Final Research Report
  • [Journal Article] On the initial value problem of the semilinear beam equation with weak damping II: asymptotic profiles2012

    • Author(s)
      Hiroshi Takeda, Shuji Yoshikawa
    • Journal Title

      Journal of Differential Equations

      Volume: 253 Issue: 11 Pages: 3061-3080

    • DOI

      10.1016/j.jde.2012.07.014

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of the steady state for multi-dimensinal thermoelastic systems Of shape memory alloys2012

    • Author(s)
      Takashi Suzuki, Shuji Yoshikawa
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series S

      Volume: 5 Pages: 209-217

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic profiles of solutions for the limit unstable Cahn-Hilliard equation with inertial term2012

    • Author(s)
      Hiroshi Takeda, Shuji Yoshikawa
    • Journal Title

      Differential and Integral Equations

      Volume: 25 Pages: 341-362

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of the steady state for multi-dimensional thermoelastic systems of shape memory alloys2012

    • Author(s)
      Takashi Suzuki, Shuji Yoshikawa
    • Journal Title

      Discrete and Continuous Dynamical Systems-Series S

      Volume: 5 Pages: 209-217

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 形状記憶合金ワイヤーの運動を記述する熱弾性方程式の導出2010

    • Author(s)
      岡部真也、鈴木貴、吉川周二
    • Journal Title

      数理解析研究所講究録

      Volume: 1693 Pages: 1-10

    • Related Report
      2010 Annual Research Report
  • [Presentation] Asymptotic profiles of solutions for the isothermal Falk-Konopka system of shape memory alloys with weak damping2012

    • Author(s)
      Shuji Yoshikawa
    • Organizer
      Linear and Nonlinear Waves, No.10
    • Place of Presentation
      Ohtsu
    • Year and Date
      2012-11-01
    • Related Report
      2012 Final Research Report
  • [Presentation] Higher order expansion of solutions for the isothermal Falk-Konopka system of shape memory alloys2012

    • Author(s)
      吉川周二
    • Organizer
      熊本大学応用解析セミナー
    • Year and Date
      2012-10-13
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] 形状記憶合金の等温 Falk-Konopka モデルの解の高次漸近形2012

    • Author(s)
      吉川周二
    • Organizer
      広島微分方程式研究会
    • Year and Date
      2012-10-06
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] Asymptotic profiles of solutions for the isothermal Falk-Konopka system with weak damping2012

    • Author(s)
      Shuji Yoshikawa
    • Organizer
      The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando, Florida
    • Year and Date
      2012-07-03
    • Related Report
      2012 Final Research Report
  • [Presentation] 形状記憶合金の等温Falk-Konopkaモデルの解の三次の漸近形2012

    • Author(s)
      吉川周二
    • Organizer
      京都駅前セミナー
    • Year and Date
      2012-06-15
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] Mathematical analysis for shape memory alloys2012

    • Author(s)
      Shuji Yoshikawa
    • Organizer
      Mathematical approach to emerging topics in materials science 2012
    • Place of Presentation
      Sendai
    • Year and Date
      2012-02-18
    • Related Report
      2012 Final Research Report
  • [Presentation] Mathematical analysis for shape memory alloys2012

    • Author(s)
      Shuji Yoshikawa
    • Organizer
      Mathemtaical approach to emerging topics in materials science 2012
    • Place of Presentation
      Tohoku University (Sendai)(招待講演)
    • Year and Date
      2012-02-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] Asymptotic profiles of solutions for the isothermal Falk-Konopka system of shape memory alloys with weak damping2012

    • Author(s)
      Shuji Yoshikawa
    • Organizer
      Linear and Nonlinear Waves, No.10
    • Place of Presentation
      大津
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic profiles of solutions for the isothermal Falk-Konopka system with weak damping2012

    • Author(s)
      Shuji Yoshikawa
    • Organizer
      The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando, Florida, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic profiles for the Falk-Konopka elastic system with weak damping2011

    • Author(s)
      Shuji Yoshikawa
    • Organizer
      The 4^<th> MSJ-SI Nonlinear Dynamics in Partial Differential Equations
    • Place of Presentation
      Kyushu University (Fukuoka)
    • Year and Date
      2011-09-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] Asymptotic profiles for the Falk-Konopka elastic system with weak damping2011

    • Author(s)
      Shuji Yoshikawa
    • Organizer
      The 4th MSJ-SI Nonlinear Dynamics in Partial Differential Equations
    • Year and Date
      2011-09-20
    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://www.me.ehime-u.ac.jp/labo/kikaiene/math/yoshikawa/

    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://www.me.ehime-u.ac.jp/labo/kikaiene/math/yoshikawa/res.html

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.me.ehime-u.ac.jp/labo/kikaiene/math/yoshikawa/res.html

    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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