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Analysis of partial differential equations arising in Material Science

Research Project

Project/Area Number 13640201
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

JIMBO Shuichi  Hokkaido Univ. Grad. School of Science, Professor, 大学院・理学研究科, 教授 (80201565)

Co-Investigator(Kenkyū-buntansha) OMATA Seiro  Kanazawa Univ. Faculty of Science, Associate Professor, 理学部, 助教授 (20214223)
MORITA Yoshihisa  Ryukoku Univ. Faculty of Science and Technology Professor, 理工学部, 教授 (10192783)
TONEGAWA Yoshihiro  Hokkaido Univ. Grad. School of Sci., Associate Professor, 大学院・理学研究科, 助教授 (80296748)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2001: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsGinzburg-Landau equation / Vortex motion / Stability analysis / Pattern formation / GL方程式 / 領域変形 / 固有値摂動 / 楕円型作用素 / 変分公式 / 特異摂動 / LL方程式 / 安定性
Research Abstract

(I) Non-trivial state solutions to the Ginzburg-Landau equation with magnetic effect are studied. Particularly, in a non-uniform thin 3-d domain, pattern is constructed (Jimbo with Morita). In 2-d convex domain, it is proved that no pattern formation exists (Jimbo with P. Sternberg).
(ii) Vortex motion in nonstationary Ginzburg-Landan equation (without magnetic effect) is studied. The reduced ODEs of vortex motion obtained by F.H. Lin and Jerrard-Soner are rewrittened in comprehensive form. The dynamics in the Neumann B.C. case is studied (Jimno and Morita).
(iii) The perturbation of eigenvalue problem of elliptic operator with discontinuous coefficients (or vaiable coefficients (or vaiable coefficients and perforated domain) is studied (Jimbo with Kosugi).
(iv) The phase transition boundary arising in the Allen-Cahn equation (with small diffusion coefficients) is studied. The regularity and the geometic property of the free boundaries are investigated (Tonegawa).
(v) The surface evolution equation driven by anisotropic effect of curvature (existence of solution and properties) is studied (Tonegawa).
(vi) Minimal surface problem with free boundary is studied. The hyperbolic evolution equation with free boundary is studied (Omata).
Numerical analysis are also done.
(vii) The vortex motion arising in the hyperbolic Ginzburg-Landau equation is studied by computational method (Omata).

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (33 results)

All Other

All Publications (33 results)

  • [Publications] S.Jimbo: "Instability in a geometric parabolic equation on convex domain"J. Differential Equations. 188. 447-460 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Jimbo: "Ginzburg-Landau functional with magnetic effect in a thin domain"Calc. Var.. 15. 325-352 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Jimbo: "Non-existence of permanent currents in convex planar samples"SIAM J. Math. Anal.. 33. 1379-1392 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Tonegawa: "Phase field model with a variable chemical potential"Proc. Royal Soc. Edingburgh SectA. 132. 993-1019 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Omata: "Numerical computations for motion of vortices governed by a hyperbolic Ginzburg-Landaw system"Nonlinear Anal. TMA. 51. 67-77 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Tonegawa: "L^P curvature and the Cauchy-Riemann equation near an isolated singular point"Nagoya Math. J.. 164. 35-51 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Tonegawa: "Higher energy solutions in the theory of phase transitions : variational approach"J. Differential Equations. 169. 190-207 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Morita: "Vortexdynamics for the Ginzburg-Landau equation with Neumann condition"Methods, Appl. Anal.. 8. 451-478 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y.Morita: "Notes on the limit equation of vortex motion for the Ginzburg-Landau equation with Neumann condition"Japan J. Indst. Appl. Math.. 18. 483-502 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Omata: "A numerical approach to the asymptotic behavior of solutions of a one-dimensional free boundary problem"JJIAM. 18. 43-58 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Omata: "Numerical calculations for the eikonal equation via the discrete Morse semi flow with Ginzburg-Landau energy"Adv. Math. Sci. Appl.. 11. 781-790 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Omata: "A numerical approach to the eikonal equation"Nonlinear Anal. TMA. 47. 3795-3802 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Jimbo: "Instability in a geometric parabolic equation on convex domain"J.Differential Equations. 188. 447-460 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Jimbo: "Ginzburg-Landau functional with magnetic effect in a thin domain"Calc.. Var.15. 325-352 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Jimbo: "Non-existence of permantent currents in convex planar samples"SIAM J. Math.Anal.. 33. 1379-1392 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Tonegawa: "Phase field model with a variable chemical potential"Royal Soc. Edingburgh Sec. A. 132. 993-1019 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Omata: "Numerical Computations for motion of voritices governed by a Hyperbolic Ginzburg-Landau System"Nonlinear Analysis TMA. 51. 67-77 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Tonegawa: "Lp-curvature and the Cauchy-Riemann equation near an isolated singular point"Nagoya Math. J.. 164. 35-51 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Tonegawa: "Higher energy solutions in the theory of phase transitions : a variational approach"J. Differential Equations. 169. 190-207 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Morita: "Vortex dynamics fot the Ginzburg-Landau equation with Neumann condition"Mathods and applcations to Analysisi. 8. 451-478 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Y. Morita: "Notes on the limit equation of vortex motion for the Ginzburg-Landau equation with Neumann condition"Japan J. Indst. Appl. Math.. 18. 483-502

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Omata: "A Numerical Approach to the Asymptotic Behavior of Solutions of a One-Dimensional Free Boundary Problem of Hyperbolic Type"JJIAM. 18. 43-58 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Omata: "Numerical calculations for the eikonal equation via the discrete Morse semiflow with Ginzburg-Landau"Adv. Math. Sci. Appl.. 11. 781-790 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S. Omata: "A numerical approach to the eikonal equation"Nonlinear Analysisi TMA. 47. 3795-3802 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] S.Jimbo: "Instability in a geometric parabolic equation on convex domain"J.Differential Equations. 188. 447-460 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Jimbo: "Non-existence of permanent currents in convex planar samples"SIAM J.Math.Anal.. 33. 1379-1392 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Morita: "Ginzburg-Landau functional with magnetic effect in a thin domain"Calc.Var.PDE. 15. 325-352 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Omata: "Numerical computations for motion of vortices governed by a hyperbolic Ginzburg-Landau system"Nonlinear Anal. TMA. 51. 67-77 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Tonegawa: "Phase field model with a variable chemcial potential"Proc.Royal Soc.Edinburgh Sect. A. 132. 993-1019 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 神保秀一: "ギンツブルグ・ランダウ方程式とボルテクス"応用数理. 11・2. 60-70 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Shuichi Jimbo: "Notes on the limit equation of vortex motion for the Ginzburg-Landau equation with Neumann condition"Japan Journal of Industrial and Applied Mathematics. 18. 483-502 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Shuichi Jimbo: "Ginzburg-Landau equation with magnetic effect in a thin domain, to appear"Calculus of Variations. (発表予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Shuichi Jimbo: "Vortex dynamics for the Ginzburg-Landau equation with Neumann condition, to appear"Method and Applications of Analysis. 8・2(発表予定). (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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