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Studies on dynamical systems of nonlinear phenomena with energy dissipation and the theory of stability

Research Project

Project/Area Number 18340045
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, 教育学部, 教授 (00033887)

Co-Investigator(Kenkyū-buntansha) ITO Akio  近畿大学, 工学部, 准教授 (30303506)
愛木 豊彦  岐阜大学, 教育学部, 准教授 (90231745)
山崎 教昭  室蘭工業大学, 工学部, 准教授 (90333658)
白川 健  神戸大学, 工学部, 講師 (50349809)
角谷 敦  広島修道大学, 経済科学部, 教授 (60248284)
深尾 武史  岐阜工業高専, 一般・講師 (00390469)
Co-Investigator(Renkei-kenkyūsha) OHARU Shinnosuke  中央大学, 理工学部, 教授 (40063721)
OTANI Mitsuharu  早稲田大学, 理工学術院, 教授 (30119656)
IMAI Hotoshi  徳島大学, 工学部, 教授 (80203298)
KADOYA Atsushi  広島修道大学, 経済科学学部, 教授 (60248284)
AIKI Toyohiko  岐阜大学, 教育学部, 准教授 (90231745)
SHIRAKAWA Ken  神戸大学, 工学部, 准教授 (50349809)
FUKAO Takeshi  京都教育大学, 教育学部, 准教授 (00390469)
YAMAZAKI Noriaki  神奈川大学, 工学部, 准教授 (90333658)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥12,740,000 (Direct Cost: ¥10,400,000、Indirect Cost: ¥2,340,000)
Fiscal Year 2009: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2008: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2007: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2006: ¥2,600,000 (Direct Cost: ¥2,600,000)
Keywordsエネルギー消散 / 非線形現象 / 相転移 / 力学系 / 変分不等式 / 力学系の安定性 / 相転移現象 / 安定性理論 / 自由境界問題 / 安定性
Research Abstract

We tried to construct a new mathematical theory for clarifying the mechanisms of nonlinear and complex phenomena in the real world and to make use of it to handle some concrete problems arising in the material and life science. In fact, our new mathematical theory provided an effective approach for some open questions. This is one of the most important achievements in this research, and the so-called "Life Mathematics" has been evolved in the same framework.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (58 results)

All 2010 2009 2008 2007 2006

All Journal Article (37 results) (of which Peer Reviewed: 28 results) Presentation (14 results) Book (7 results)

  • [Journal Article] Mathematical treatment of concrete carbonation process--a moving one-phase approach2010

    • Author(s)
      T. Aiki, A. Muntean
    • Journal Title

      Gakuto Intern.Ser.Math.Sci.Appl. Vol. 32

      Pages: 231-238

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global attractor of double obstacle problem in thermohydraulics2010

    • Author(s)
      T. Fukao, M. Kubo
    • Journal Title

      Gakuto Intern.Ser.Math.Sci.Appl. Vol. 32

      Pages: 273-287

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal control problems for regional economic trends2010

    • Author(s)
      A. Kadoya, A. Ito, K. Shirakawa
    • Journal Title

      Gakuto Intern.Ser.Math.Sci.Appl. Vol. 32

      Pages: 327-340

    • Related Report
      2009 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

      Gakuto Intern.Ser.Math.Sci.Appl. Vol. 32

      Pages: 389-403

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Two-dimensional steady-state solutions anisotropic total variation flows associated with phase transitions2010

    • Author(s)
      K. Shirakawa
    • Journal Title

      Gakuto Intern.Ser.Math.Sci.Appl. Vol. 32

      Pages: 483-504

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear evolution equations generated by subdifferentials with nonlocal constraints2009

    • Author(s)
      R. Kano, N. Kenmochi, Y. Murase
    • Journal Title

      Polish Acad. Sci., Inst.Math.(Banach Center Publ.) Vol. 86

      Pages: 175-194

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Elliptic quasi-variational inequalities and applications2009

    • Author(s)
      Y. Murase, R. Kano, N. Kenmochi
    • Journal Title

      Discrete & Continuous Dynamical Systems-Supplement

      Pages: 583-591

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak solutions of grain boundary motion model with singularity2009

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

      Rendiconti di Mat., Ser.VII, Univ.di Roma, Italy Vol. 29

      Pages: 51-63

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures2009

    • Author(s)
      T. Aiki, A. Muntean
    • Journal Title

      Adv.Math.Sci.Appl. Vol. 19

      Pages: 109-129

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model2009

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

      Polish Acad.Sci., Inst.Math.(Banach Center Publ.) Vol. 86

      Pages: 45-58

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies2009

    • Author(s)
      K. Shirakawa
    • Journal Title

      Polish Acad.Sci., Inst.Math.(Banach Center Publ.) Vol. 86

      Pages: 287-302

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak solutions of grain boundary motion model with singularity2009

    • Author(s)
      伊藤昭夫、剣持信幸、山崎教昭
    • Journal Title

      Rendiconti di Mat., Ser.VII, Univ.di Roma, Italy 29

      Pages: 51-63

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear evolution equations generated by subdifferentials with nonlocal constraints2009

    • Author(s)
      加納理成、剣持信幸、村瀬勇介
    • Journal Title

      Banach Center Publ.(Polish Acad.Sci.) 86

      Pages: 175-194

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Elliptic quasi-variational inequalities and applications2009

    • Author(s)
      村瀬勇介、加納理成、剣持信幸
    • Journal Title

      Discrets & Continuous Dynamical Systems 増刊号

      Pages: 583-591

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A phase-field model of grain boundary motion2008

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

      Appl.Math. Vol. 53

      Pages: 433-454

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A mathematical model for bacteria growth2008

    • Author(s)
      T. Aiki, J. Kopfova
    • Journal Title

      World Scientific(ed. M. Chipot, C.-S. Lin and D.-H. Tsai)

      Pages: 1-10

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Free boundary problems of the nonlinear heat equations coupled with Navier-Stokes equations2008

    • Author(s)
      T. Fukao
    • Journal Title

      World Scientific(ed. M. Chipot, C.-S. Lin and D.-H. Tsai)

      Pages: 67-76

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A class of doubly nonlinear evolution equations in Hilbert spaces2008

    • Author(s)
      R. Kano, N. Kenmochi, Y. Murase
    • Journal Title

      Adv.Math.Sci.Appl. Vol. 18

      Pages: 381-399

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of the solution to the non-isothermal phase separation2008

    • Author(s)
      A. Ito, T. Suzuki
    • Journal Title

      Nonlinear Analysis Vol. 68

      Pages: 1825-1843

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence theorems for elliptic quasi-variational inequalities in Banach spaces2008

    • Author(s)
      R.Kano,Y.Murase, N.Kenmochi
    • Journal Title

      in Recent Advances in Nonlinear Analysis, World Scientific

      Pages: 149-169

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] A phase-field model of grain boundary motion2008

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

      Appl. Math. Vol.53

      Pages: 433-454

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] A phase-field model of grain boundary motion2008

    • Author(s)
      伊藤昭夫、剣持信幸、山崎教昭
    • Journal Title

      Application of Mathematics 53

      Pages: 433-454

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A class of doubly nonlinear evolution equations in Hilbert spaces2008

    • Author(s)
      加納理成、剣持信幸、村瀬勇介
    • Journal Title

      Advances in Mathematical Sciences and Applications 18

      Pages: 381-399

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence for a class of nonlocal quasivariational evolution problems2008

    • Author(s)
      剣持信幸,U. Stefanelli
    • Journal Title

      Gakuto International Series, Mathematical Sciences and Applications 29

      Pages: 253-264

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence theorems for elliptic quasi-variational inequalities in Banach spaces2008

    • Author(s)
      剣持 信幸, 加納 理成, 村瀬 勇介
    • Journal Title

      Recent Advances in Nonlinear Analysis、World Scientific

      Pages: 149-169

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Phase separation model of Penrose-Fife type with Signorini boundary condition2007

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

      Adv.Math.Sci.Appl. Vol. 17

      Pages: 337-356

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A free boundary problem for an elastic material2007

    • Author(s)
      T. Aiki
    • Journal Title

      Dynamical Systems, Applications, supplement, 2007, AIMS

      Pages: 10-17

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase separation model of Penrose-Fife type with Signorini boundary condition2007

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

      Advances in Mathematical Sciences and Applications Vol.17

      Pages: 337-356

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Damage problems for viscous locking materials2006

    • Author(s)
      M. Fremond, N. Kenmochi
    • Journal Title

      Adv.Math.Sci.Appl. Vol. 16

      Pages: 697-716

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Solvability for a PDE model of regional economic trend2006

    • Author(s)
      K. Shirakawa, A. Ito, A. Kadoya
    • Journal Title

      "Free Boundary Problems : Theory and Applications", ISNM Vol. 154

      Pages: 403-412

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Parabolic systems with the unknown dependent constraints arising in phase transitions2006

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

      in Free Boundary Problems: Theory and Applications Vol.154(ISNM)

      Pages: 45-54

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Parabolic systems with the unknown dependent constraints arising in phase transitions2006

    • Author(s)
      阿曽雅泰
    • Journal Title

      ISNM Free Boundary Problems : Theory and Applications 154

      Pages: 45-54

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Damage problems for viscous locking materials2006

    • Author(s)
      M.Fremond
    • Journal Title

      Advances in Mathematical Sciences and Applications 16

      Pages: 697-716

    • Related Report
      2006 Annual Research Report
  • [Journal Article] One-dimensional shape memory alloy problem with Duhem type of hysteresis operators2006

    • Author(s)
      愛木豊彦
    • Journal Title

      ISNM Free Boundary Problems : Theory and Applications 154

      Pages: 1-10

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Solvability for a PDE model of regional economic trend2006

    • Author(s)
      白川健
    • Journal Title

      ISNM Free Boundary Problems : Theory and Applications 154

      Pages: 403-412

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Mathematical models including a hysteresis operator2006

    • Author(s)
      愛木豊彦
    • Journal Title

      Series on Advances in Mathematics for Applied Sciences, Dissipative Phase Transitions 71

      Pages: 1-18

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Weak solutions for Stefan problems with convections2006

    • Author(s)
      深尾武史
    • Journal Title

      Series on Advances in Mathematics for Applied Sciences, Dissipative Phase Transitions 71

      Pages: 87-99

    • Related Report
      2006 Annual Research Report
  • [Presentation] Dynamical System Associated with Grain Boundary Motion2009

    • Author(s)
      剣持信幸
    • Organizer
      Conference on Evolution Equations, Related Topics and Applications
    • Place of Presentation
      ミュンヘン工科大、ドイツ
    • Year and Date
      2009-09-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] Dynamical system associated with grain boundary motion2009

    • Author(s)
      N. Kenmochi
    • Organizer
      Conference on "Evolution Equations, Related Topics and Applications"
    • Place of Presentation
      Munich, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] A model of grain boundary motion2009

    • Author(s)
      N. Kenmochi
    • Organizer
      Perspectives in PDEs
    • Place of Presentation
      Univ. Roma "LaSapienza", Italy
    • Related Report
      2009 Final Research Report
  • [Presentation] Quasi-variational evolution problems2008

    • Author(s)
      N., Kenmochi
    • Organizer
      7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Arlington Texas USA
    • Year and Date
      2008-05-20
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Quasi-variational evolution problems2008

    • Author(s)
      剣持信幸
    • Organizer
      7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      テキサス大学、USA
    • Year and Date
      2008-05-20
    • Related Report
      2008 Annual Research Report
  • [Presentation] A class of quasivariational inequalities for phase transitions2008

    • Author(s)
      N. Kenmochi
    • Organizer
      Workshop on "PDE Approximations in Fast Reaction-Slow Diffusion Scenario"
    • Place of Presentation
      Netherlands
    • Related Report
      2009 Final Research Report
  • [Presentation] A variational inequality for grain boundary motion2008

    • Author(s)
      N. Kenmochi
    • Organizer
      Workshop on "Phase Transitions and Optimal Control"
    • Place of Presentation
      Berlin, WIAS, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] Some remarks on quasivariational problems2008

    • Author(s)
      N. Kenmochi
    • Organizer
      WCNA2008 Minisymposia (Nonlinear Evolution Equations, Applications and Related Topics)
    • Place of Presentation
      Orland, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] Quasi-variational evolution problems2008

    • Author(s)
      N. Kenmochi
    • Organizer
      The 7th AIMS, Session on Nonlinear Evolution Equations and Related Topics
    • Place of Presentation
      Arlington, Texas, USA
    • Related Report
      2009 Final Research Report
  • [Presentation] Recent development of parabolic quasi-vahational inequalities2007

    • Author(s)
      剣持 信幸
    • Organizer
      国際ワークショップ "Nonlocal and Abstract Parabolic Equations and their Applications"
    • Place of Presentation
      Bedlewo,Poland
    • Year and Date
      2007-07-26
    • Related Report
      2007 Annual Research Report
  • [Presentation] Recent development of evolution equations in free boundary problems, Symposium in honour of Prof.2007

    • Author(s)
      N. Kenmochi
    • Organizer
      Technical University of Munich(K.-H. Hoffmann)
    • Place of Presentation
      Munich, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] Recent development of parabolic variational inequalities2007

    • Author(s)
      N. Kenmochi
    • Organizer
      Workshop on Nonlocal and Abstract Parabolic Equations and their Applications
    • Place of Presentation
      Bedlewo, Poland
    • Related Report
      2009 Final Research Report
  • [Presentation] A class of doubly nonlinear evolution equations in Hilbert spaces2006

    • Author(s)
      N. Kenmochi
    • Organizer
      NCTS International Conference on Nonlinear Analysis, NCTS
    • Place of Presentation
      Hsinchu, Taiwan
    • Related Report
      2009 Final Research Report
  • [Presentation] A class of doubly nonlinear systems for phase transitions2006

    • Author(s)
      N. Kenmochi
    • Organizer
      The 6th AIMS, Session on Dynamical Systems Associated with Nonlinear Phenomena with Energy Dissipation
    • Place of Presentation
      Poitiers, France
    • Related Report
      2009 Final Research Report
  • [Book] Nonlinear evolution equations, related topics and applications, Gakuto International Series, Mathematical Sciences and Applications2010

    • Author(s)
      愛木豊彦, 剣持信幸, (他2名)
    • Total Pages
      517
    • Related Report
      2009 Final Research Report
  • [Book] Current Advances in Nonlinear Analysis and Related Topics(Gakuto Intern.Ser.Math.Sci.Appl.,Vol.32)2010

    • Author(s)
      愛木豊彦、剣持信幸、大谷光春、M.Niezgodka
    • Total Pages
      517
    • Publisher
      学校図書(株)
    • Related Report
      2009 Annual Research Report
  • [Book] Nonlinear phenomena with energy dissipation : athematical analysis, modeling and simulation, Gakuto International Series, Mathematical Sciences and Applications2008

    • Author(s)
      P. Colli, 剣持信幸, (他3名)
    • Total Pages
      475
    • Related Report
      2009 Final Research Report
  • [Book] Mathematical Sciences and Applications Vol.292008

    • Author(s)
      P.Colli, A.Damlamian, N.Kenmochi, M.Mimura, J.Sprekels ura,J.Sprekels
    • Total Pages
      475
    • Publisher
      Nonlinear Phenomena with Energy Dissipation : Mathematical Analysis and Simulation(Gakuto International Series)
    • Related Report
      2008 Self-evaluation Report
  • [Book] Nonlinear phenomena with energy dissipation: Mathematical Analysis, modeling and simulation2008

    • Author(s)
      P.CQlli, A.Damlamian,剣持信幸(他2名)
    • Total Pages
      475
    • Publisher
      学校図書(株)
    • Related Report
      2008 Annual Research Report
  • [Book] Monotonicity and compactness methods for nonlinear variational inequalities(Chap.4) Handbook of Differential Equations, Stationary Partial Differential Equations Vol.42007

    • Author(s)
      剣持 信幸
    • Publisher
      Elsevier B.V.
    • Related Report
      2007 Annual Research Report
  • [Book] Series on Advances in Mathematics for Applied Sciences Vol.71, Dissipative Phase Transitions2006

    • Author(s)
      P.Colli
    • Total Pages
      298
    • Publisher
      World Scientific Publishing Co. Pte. Ltd
    • Related Report
      2006 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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