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Study of problems in calculus of variations, differential equations, and other areas involving minimizing movements

Research Project

Project/Area Number 19540212
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KIKUCHI Koji  Shizuoka University, 工学部, 教授 (50195202)

Co-Investigator(Kenkyū-buntansha) SHIMIZU Senjo  静岡大学, 理学部, 教授 (50273165)
HOSHIGA Akira  静岡大学, 工学部, 准教授 (60261400)
ADACHI Shinji  静岡大学, 工学部, 准教授 (40339685)
NAKAJIMA Toru  静岡大学, 工学部, 准教授 (50362182)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsミニマイジング・ムーブメント / 変分問題 / 非線形偏微分方程式 / 発展方程式 / 幾何学的測度論
Research Abstract

Through this study we obtain that the limit of approximate solutions to the equation of vibrating string with an obstacle is really a solution to this equation. Besides we obtain several facts in the study of the equation of motion of a vibrating nonparametric membrane, in the study of a system of quasilinear hyperbolic equations, in the study of gradient Young measures for BV functions, in the study of the equation of motion of a vibrating membrane with a strong viscosity term.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report

Research Products

(23 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (14 results) (of which Peer Reviewed: 13 results) Presentation (9 results)

  • [Journal Article] G-invariant positive solutions for a quasilinear Schrodinger equation2011

    • Author(s)
      Shinji Adachi, Tatsuya Watanabe
    • Journal Title

      Adv.Differential Equations

      Volume: 16 Pages: 289-324

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] End-point maximal regularity and its application to two-dimensional Keller-Segel system2010

    • Author(s)
      Takayoshi Ogawa, Senjo Shimizu
    • Journal Title

      Math.Z

      Volume: 264 Pages: 601-628

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Constructing a solution in time semidiscretization method to an equation of vibrating string with an obstacle2009

    • Author(s)
      Koji Kikuchi
    • Journal Title

      Nonlinear Analysis 71

    • NAID

      120002165422

    • URL

      http://ir.lib.shizuoka.ac.jp/handle/10297/5035

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Constructing a solution in time semidiscretization Method to an equation of vibrating string with an obstacle2009

    • Author(s)
      Koji Kikuchi
    • Journal Title

      Nonlinear Analysis 71

    • NAID

      120002165422

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a resolvent estimate of the Stokes system in a half-space arising from a free boundary problem for the Navier-Stokes equations2009

    • Author(s)
      Yoshihiro Shibata, Senjo Shimizu
    • Journal Title

      Math. Nachr. 282巻

      Pages: 482-499

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A remark on instability of harmonic maps betweenspheres2009

    • Author(s)
      To^ru Nakajima
    • Journal Title

      Pacific J. Math. 240巻

      Pages: 363-369

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear approximation for equations of motion of vibrating membrane with one parameter2008

    • Author(s)
      Koji Kikuchi
    • Journal Title

      J.Math.Soc.Japan 60

      Pages: 127-169

    • NAID

      10024331474

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report 2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The drift-diffusion system in two-dimensional critical Hardy space2008

    • Author(s)
      Takayoshi Ogawa, Senjo Shimizu
    • Journal Title

      J. Funct. Anal. 255巻

      Pages: 157-209

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space2008

    • Author(s)
      Akira Hoshiga
    • Journal Title

      Hokkaido Math. J. 37巻

      Pages: 669-688

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the L_pL_q maxmal regularity of the Neumann problem for the Stokes equations in a bounded domain2008

    • Author(s)
      Y.Shibata and S.Shimizu
    • Journal Title

      J.Refine Angew.Math. 615

      Pages: 157-210

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] L_p-L_q maximal regularity of the Neumann problem for the Stokesequations in a bounded domain2007

    • Author(s)
      Y.Shibata and S.Shimizu
    • Journal Title

      Advanced Studies in Pure Mathematics 47

      Pages: 349-362

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Free boundary problems for a viscous incompressible fluid2007

    • Author(s)
      Y.Shibata and S.Shimizu
    • Journal Title

      Proceedings of the Kyoto Conference on the Navier-Stokes Equations and their Applications, RIMS Kokyuroku Bessatsu B1

      Pages: 343-358

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] L_p-L_q maximal regularity of the interface problem fcr the Stokes system in a bounded domain2007

    • Author(s)
      Y.Shibata and S.Shimizu
    • Journal Title

      RIMS Kokyuroku 1536

      Pages: 58-72

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Constructing a solution in time semidiscretization Method to an equation of vibrating string with anobstacle

    • Author(s)
      Koji Kikuchi
    • Journal Title

      Nonlinear Analysis (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 一階対称双曲系の解の構成について2011

    • Author(s)
      菊地光嗣
    • Organizer
      数理科学セミナー
    • Place of Presentation
      茨城大学
    • Year and Date
      2011-03-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] 一次増大度の粘性項を持つ膜の振動方程式について2010

    • Author(s)
      菊地光嗣
    • Organizer
      夏の偏微分方程式セミナー2010
    • Place of Presentation
      神戸大学
    • Year and Date
      2010-08-25
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 有界変動函数列の収束について2009

    • Author(s)
      菊地光嗣
    • Organizer
      夏の偏微分方程式セミナー2009
    • Place of Presentation
      竜谷大学セミナーハウス
    • Year and Date
      2009-08-29
    • Related Report
      2009 Annual Research Report 2009 Self-evaluation Report
  • [Presentation] An analysis of a system of quasilinear hyperbolic equations having quasiconvex and linear growth energy functional2008

    • Author(s)
      菊地光嗣
    • Organizer
      熊本における偏微分方程式研究集会
    • Place of Presentation
      熊本大学大学院自然科学研究科
    • Year and Date
      2008-10-25
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] An analysis of a system of quasilinear hyperbolic equations having quasiconvex and linear growth energy functional2008

    • Author(s)
      菊地光嗣
    • Organizer
      第9回広島応用解析セミナー
    • Place of Presentation
      広島大学工学部
    • Year and Date
      2008-09-04
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report 2008 Annual Research Report
  • [Presentation] A remark on BV functions2008

    • Author(s)
      Koji Kikuchi
    • Organizer
      Hamamatsu Workshop on Nonlinear Evolution Equations 2007
    • Place of Presentation
      静岡県立森林公園 森の家
    • Year and Date
      2008-08-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Constructing a solution in time semidiscretization method to an equation of vibrating string with an obstacle2008

    • Author(s)
      菊地光嗣
    • Organizer
      WCNA2008
    • Place of Presentation
      米国フロリダ州
    • Year and Date
      2008-07-08
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Constructing a solution in minimizing movement method to an equation of vibrating string with an obstacle2007

    • Author(s)
      菊地光嗣
    • Organizer
      Kumamoto Workshop on Nonlinear Evolution Equations 2007
    • Place of Presentation
      休暇村南阿蘇
    • Year and Date
      2007-08-10
    • Related Report
      2010 Final Research Report
  • [Presentation] Constructing a solution in mhlimizing movement method to an equation of vibrating string with an obstacle2007

    • Author(s)
      Koji Kikuchi
    • Organizer
      Kumamoto Workshop on Nonlinear Evolution Equations 2007
    • Place of Presentation
      休暇村南阿蘇
    • Year and Date
      2007-08-10
    • Related Report
      2007 Annual Research Report

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Published: 2007-03-31   Modified: 2016-04-21  

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