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Singular domain deformation and analysis on elliptic operators in elasticity and electromagnetism

Research Project

Project/Area Number 25400153
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research InstitutionHokkaido University

Principal Investigator

Jimbo Shuichi  北海道大学, 理学(系)研究科(研究院), 教授 (80201565)

Co-Investigator(Kenkyū-buntansha) HONDA NAOFUMI  北海道大学, 大学院理学研究院, 教授 (00238817)
TONEGAWA YOSHIHIRO  東京工業大学, 理工学研究科, 教授 (80296748)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords特異的領域変形 / 楕円型作用素 / 固有値問題 / ラプラス作用素 / ストークス作用素 / ラメ作用素 / スペクトル / マックスウェルの作用素 / 固有振動 / 摂動公式 / 領域変形
Outline of Final Research Achievements

I studied spectra of elliptic operators for regularly or singularly deformed domain (Lame operator, Stokes operator, Maxwell operator). (i) I studied polynomial solutions, rational type solutions with their structures of homogeneous Stokes and Elastic equations (with H.Ito, N.Honda), (ii) I obtained spectral Hadamard variational formula of Stokes operator, Maxwell operator for regularly perturbed domain for Dirichlet and Slip type boundary condition (with E. Ushikoshi). I obtained an elaborate behaviors of eigenvalues for Maxwell operator, (iii) I studied elaborate behaviors of eigenvalues of Lame or Maxwell operators in a domain with small hole, (iv) I obtained elaborate behaviors of eigenfrequencies of elastic body composed of several thin rod.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (14 results)

All 2016 2015 2014 2013

All Journal Article (8 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 8 results,  Acknowledgement Compliant: 2 results,  Open Access: 1 results) Presentation (6 results) (of which Int'l Joint Research: 1 results,  Invited: 5 results)

  • [Journal Article] Hadamard variational formula for the eigenvalue of the Stokes equations with the Dirichlet boundary conditions2015

    • Author(s)
      S. Jimbo, E. Ushikoshi
    • Journal Title

      Far East Journal of Mathematical Sciences

      Volume: 98 Pages: 713-739

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of the Laplacian in a domain with a thin tubular hole2015

    • Author(s)
      S. Jimbo
    • Journal Title

      Journal of Elliptic and Parabolic Equations

      Volume: 1 Pages: 137-174

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral comparison and gradient-like property in the Fitz-Nagumo type Equations2015

    • Author(s)
      C.N. Chen, S. Jimbo, Y. Morita
    • Journal Title

      Nonlinearity

      Volume: 28 Pages: 1003-1016

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the geometric aspect of Sato's postulates on the S-matrix2015

    • Author(s)
      N. Honda, T. Kawai, H.P. Stapp
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B52 Pages: 11-54

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Convergence of the Allen-Cahn equation with Neumann boundary conditions2015

    • Author(s)
      M. Mizuno, Y. Tonegawa
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 47 Pages: 1906-1932

    • NAID

      120006459746

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral comparison and gradient-like property2015

    • Author(s)
      Chao-Nien Chen, Shuichi Jimbo, and Yoshihisa Morita
    • Journal Title

      Nonlinearity

      Volume: 28 Issue: 4 Pages: 1003-1016

    • DOI

      10.1088/0951-7715/28/4/1003

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Hadamard Variation for Electromagnetic Frequencies2013

    • Author(s)
      Shuichi JIMBO
    • Journal Title

      Geometric Properties for Parabolic and Elliptic PDE's,

      Volume: 2 Pages: 179-199

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lyapunov function and spectrum comparison for a reaction-diffusion system with mass conservation2013

    • Author(s)
      Shuichi Jimbo, Yoshihisa Morita
    • Journal Title

      J. Differential Equations

      Volume: 255 Pages: 1657-1683

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Reaction diffusion equations in an infinite Y-shaped Graph and a time entire solutions2016

    • Author(s)
      Shuichi Jimbo
    • Organizer
      Geometry of PDEs and its related Problems
    • Place of Presentation
      Tohoku University, Miyagi prefecture, Sendai city
    • Year and Date
      2016-10-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 特異的領域変形と固有値問題2015

    • Author(s)
      神保秀一
    • Organizer
      パターン形成とダイナミクスの解構造の探求
    • Place of Presentation
      学術交流会館, 北海道大学, 北海道, 札幌市
    • Year and Date
      2015-06-26
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Spectra of domains with a thin tubular hole2015

    • Author(s)
      Shuichi Jimbo
    • Organizer
      Colloquim
    • Place of Presentation
      Inha University, Incheon, Korea
    • Year and Date
      2015-04-28
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Eigenvalues of the Laplacian in a domain with a thin tubular hole2014

    • Author(s)
      Shuichi JIMBO
    • Organizer
      2014NCTS Workshop on Calculus of Variations and Related topics
    • Place of Presentation
      NCTS National Tsing-Hua Univ.(台湾)
    • Year and Date
      2014-10-29 – 2014-10-31
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Eigenvalues of the Laplacian in a domain with a thin tubular hole2014

    • Author(s)
      Shuichi JIMBO
    • Organizer
      8th European Conference on Elliptic and Parabolic Problems
    • Place of Presentation
      Hotel Serapo(Gaeta, Italy)
    • Year and Date
      2014-05-26 – 2014-05-30
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Eigenvalues of Laplacian in a domain with a thin tubular hole2013

    • Author(s)
      Shuichi JIMBO
    • Organizer
      日本数学会, 応用数学分科会
    • Place of Presentation
      愛媛大学, 松山市
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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