• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Analysis of mathematical model of grain boundary motions in materials and evolution of mathematical theory

Research Project

Project/Area Number 22740110
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionKanagawa University

Principal Investigator

YAMAZAKI NORIAKI  神奈川大学, 工学部, 教授 (90333658)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords関数方程式 / 非線形解析 / 非線形現象 / 自由境界 / 最適制御 / 関数方程式論 / 実函数論 / 力学系 / 相転移現象 / 特異拡散 / 実函教諭
Research Abstract

In this research project, we consider mathematical models of grain boundary motions in materials, which is a Kobayashi-Warren-Carter type. Then, we showed the asymptotic behavior of solutions, the existence and stability of stationary solutions and the existence and characterization of attractors. Also, we proved the solvability of the original Kobayashi-Warren-Carter model of grain boundary motions. Moreover, we showed the existence of solutions to a system of Allen-Cahn equation and grain boundary motion model of Kobayashi-Warren-Carter type. Also, we studied optimal control problems for phase field system with total variation functional as the interfacial energy. Then, we proved the existence of an optimal control that minimizes the nonlinear and nonsmooth cost functional. Moreover, we showed the necessary condition of the optimal pair.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (31 results)

All 2013 2012 2011 2010

All Journal Article (14 results) (of which Peer Reviewed: 13 results) Presentation (17 results) (of which Invited: 1 results)

  • [Journal Article] Global attractors for non-autonomous phase-field systems of grain boundary motion with constraint2013

    • Author(s)
      N. Yamazaki
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 23 Pages: 267-296

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Solvability for one-dimensional phase field system associated with grain boundary motion2013

    • Author(s)
      K. Shirakawa, H. Watanabe and N. Yamazaki
    • Journal Title

      Mathematische Annalen

      Volume: 356 Pages: 301-330

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal control problems of phase field system with total variation functional as the interfacial energy2013

    • Author(s)
      K. Shirakawa and N. Yamazaki
    • Journal Title

      Advances in Differential Equations

      Volume: 18 Pages: 309-350

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal control problem of positive solutions to second order impulsive differential equations2012

    • Author(s)
      L. Zhang, N. Yamazaki and C. Zhai
    • Journal Title

      Zeitschrift fur Analysis und ihre Anwendungen

      Volume: 31 Pages: 237-250

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Variational inequalities for a system of elliptic-parabolic equations2012

    • Author(s)
      M. Kubo, K. Shirakawa and N. Yamazaki
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 387 Pages: 490-511

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal control problem for Allen-Cahn type equation associated with total variation energy2012

    • Author(s)
      T. Ohtsuka, K. Shirakawa and N. Yamazaki
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series S

      Volume: 5 Pages: 159-181

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solvability of a model for grain boundary motion with constraint2012

    • Author(s)
      A. Ito, N. Kenmochi and N. Yamazaki
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series S

      Volume: 5 Pages: 127-146

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solvability of a model for grain boundary motion with constraint2012

    • Author(s)
      A. Ito, N. Kenmochi and N. Yamazaki
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series S

      Volume: 5

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal control problem for Allen-Cahn type equation associated with total variation energy2012

    • Author(s)
      T. Ohtsuka, K. Shirakawa and N. Yamazaki
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series S

      Volume: 5

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global attractor of the multivalued semigroup associated with a phase-field model of grain boundary motion with constraint2011

    • Author(s)
      N. Kenmochi and N. Yamazaki
    • Journal Title

      Dynamical Systems, Differential Equations and Applications, Discrete and Continuous Dynamical Systems

      Volume: Volume II Pages: 824-833

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global attractor of the multivalued semigroup associated with a phase-field model of grain boundary motion with constraint2011

    • Author(s)
      N.Kenmochi, N.Yamazaki
    • Journal Title

      Dynamical Systems, Differential Equations and Applications, Volume II, Discrete and Continuous Dynamical Systems

      Volume: A Supplement Volume Pages: 824-833

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability for a grain boundary motion model with constraint2011

    • Author(s)
      剣持信幸, 山崎教昭
    • Journal Title

      数理解析研究所講究録1746,現象の数理解析へ向けた非線形発展方程式とその周辺,京都大学数理解析研究所

      Volume: 1746 Pages: 1-21

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Large-time behavior of solutions to a phase-field model of grain boundary motion with constraint, Current Advances in Nonlinear Analysis and Related Topics2010

    • Author(s)
      N. Kenmochi and N. Yamazaki
    • Journal Title

      GAKUTO Internat. Ser. Math. Sci. Appl

      Volume: 32 Pages: 389-403

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Large-time behavior of solutions to a phase-field model of grain boundary motion with constraint2010

    • Author(s)
      N.Kenmochi, N.Yamazaki
    • Journal Title

      Current Advances in Nonlinear Analysis and Related Topics, GAKUTO Internat.Ser.Math.Sci.Appl.

      Volume: 32 Pages: 389-403

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Control problems of phase-field systems associated with total variation energy2013

    • Author(s)
      山崎教昭, 白川健
    • Organizer
      日本数学会2013年度秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-25
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Necessary conditions for optimal control of positive solutions to second order impulsive differential equations2013

    • Author(s)
      山崎教昭, L. Zhang, C. Zhai
    • Organizer
      日本数学会2013年度年会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Optimal control of positive solutions to second order impulsive diifferential equations2012

    • Author(s)
      山崎教昭, L. Zhang, C. Zhai
    • Organizer
      日本数学会2012年度秋季総合分科会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Optimal control problem of positive solutions to second order impulsive differential equations2012

    • Author(s)
      N. Yamazaki, L. Zhang, C. Zhai
    • Organizer
      The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      the Hyatt Grand Cypress Resort, Orlando, Florida, アメリカ
    • Year and Date
      2012-07-01
    • Related Report
      2013 Final Research Report
  • [Presentation] A vector-valued elliptic-parabolic variational inequality with time-dependent constraint2012

    • Author(s)
      山崎教昭, 久保雅弘, 白川健
    • Organizer
      日本数学会2012年度年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Optimal control problems of phase field system with total variation functional as the interfacial energy2012

    • Author(s)
      N. Yamazaki, K. Shirakawa
    • Organizer
      12. International Conference on Free Boundary Problems, Theory and Applications
    • Place of Presentation
      Frauenchiemsee, Chiemsee, ドイツ
    • Related Report
      2013 Final Research Report
  • [Presentation] Optimal control problems of phase field system with total variation functional as the interfacial energy2012

    • Author(s)
      N. Yamazaki
    • Organizer
      12. International Conference on Free Boundary Problems, Theory and Applications
    • Place of Presentation
      ドイツ
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Some characterization of attractor for a grain boundary motion model with constraint2011

    • Author(s)
      山崎教昭, 剣持信幸
    • Organizer
      日本数学会2011年度秋季総合分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-29
    • Related Report
      2013 Final Research Report 2011 Annual Research Report
  • [Presentation] Global attractor of a grain boundary motiom model with constraint2011

    • Author(s)
      山崎教昭, 剣持信幸
    • Organizer
      日本数学会2011年度年会
    • Place of Presentation
      早稲田大学
    • Related Report
      2013 Final Research Report 2011 Annual Research Report
  • [Presentation] Asymptotic stability for a grain boundary motion model with constraint2010

    • Author(s)
      山崎教昭, 剣持信幸
    • Organizer
      現象の数理解析に向けた非線形発展方程式とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Asymptotic stability for a grain boundary motion model with constraint2010

    • Author(s)
      N.Yamazaki
    • Organizer
      RIMS研究集会「現象の数理解析に向けた非線形発展方程式とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Large-time behavior of solutions to a grain boundary motion models with constraint2010

    • Author(s)
      山崎教昭, 剣持信幸
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Kobayashi-Warren-Carter型結晶粒界モデルの解の漸近挙動について2010

    • Author(s)
      山崎教昭
    • Organizer
      第5回さいたま数理解析セミナー
    • Place of Presentation
      埼玉大学サテライトキャンパス
    • Year and Date
      2010-09-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Mathematical analysis of grain boundary motion models of Kobayashi-Warren-Carter type2010

    • Author(s)
      N. Yamazaki
    • Organizer
      Tutorial Lectures and International Workshop "Singular Diffusion and Evolving Interfaces"
    • Place of Presentation
      北海道大学, Sapporo, 日本
    • Year and Date
      2010-08-02
    • Related Report
      2013 Final Research Report
  • [Presentation] Mathematical analysis of grain boundary motion models of Kobayashi-Warren-Carter type2010

    • Author(s)
      N.Yamazaki
    • Organizer
      Tutorial Lectures and International Workshop "Singular Diffusion and Evolving Interfaces"
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-08-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] Global attractor of a phase-field model of grain boundary motion with constraint2010

    • Author(s)
      N. Yamazaki, N. Kenmochi
    • Organizer
      The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      The Dresden University of Technology, Dresden, ドイツ
    • Year and Date
      2010-05-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Global attractor of a phase-field model of grain boundary motion with constraint2010

    • Author(s)
      N.Kenmochi, N.Yamazaki
    • Organizer
      The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Dresden University of Technology,ドイツ
    • Year and Date
      2010-05-25
    • Related Report
      2010 Annual Research Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi