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

Development of mathematical analysis via phase field method

Research Project

Project/Area Number 21340033
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

TONEGAWA Yoshihiro  北海道大学, 大学院・理学研究院, 教授 (80296748)

Co-Investigator(Kenkyū-buntansha) NISHIURA Yasumasa  東北大学, 原子分子材料科学高等研究機構, 教授 (00131277)
Co-Investigator(Renkei-kenkyūsha) OKABE Shinya  東北大学, 大学院・理学研究科, 准教授 (70435973)
MAEKAWA Yasunori  東北大学, 大学院・理学研究科, 准教授 (70507954)
Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥15,080,000 (Direct Cost: ¥11,600,000、Indirect Cost: ¥3,480,000)
Fiscal Year 2012: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2010: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2009: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
KeywordsAllen-Cahn方程式 / Cahn-Hilliard方程式 / フェイズフィールド法 / 変分法 / 平均曲率流 / 幾何学的測度論 / 極小曲面 / 相分離 / 平均曲率
Research Abstract

A family of smooth surfaces parameterized by time is called mean curvature flow if the velocity of motion at each point and time is equal to its mean curvature vector. We have made fundamental advance of knowledge on the general existence and regularity theory of mean curvature flow which may have singularities, and moreover, on those of geometric time evolution problems in large.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (59 results)

All 2014 2013 2012 2011 2010 2009 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (49 results) (of which Invited: 5 results) Remarks (3 results)

  • [Journal Article] A second derivative Hoelder estimate for weak mean curvature flow2014

    • Author(s)
      Y. Tonegawa
    • Journal Title

      Advances in Calculus of Variations

      Volume: 7 Issue: 1 Pages: 91-138

    • DOI

      10.1515/acv-2013-0104

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A general regularity theory for weak mean curvature flow2014

    • Author(s)
      K. Kasai and Y. Tonegawa
    • Journal Title

      Calc. Var. Partial Differential Equations

      Volume: 50 Issue: 1-2 Pages: 1-68

    • DOI

      10.1007/s00526-013-0626-4

    • NAID

      120005600747

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Two-phase flow problem coupled with mean curvature flow2012

    • Author(s)
      Liu,C.,Sato,N.,Tonegawa,Y
    • Journal Title

      Interfaces and Free Boundaries

      Volume: 14 Issue: 2 Pages: 185-203

    • DOI

      10.4171/ifb/279

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stable phase interfaces in the van der Waals-Cahn-Hilliard theory2012

    • Author(s)
      Tonegawa, Y., Wickramasekera, N
    • Journal Title

      Journal fur Reine und Angewandte Mathematik

      Volume: 668 Issue: 668 Pages: 191-210

    • DOI

      10.1515/crelle.2011.134

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The variational problem for a certain space-time functional defined on planar closed curves2012

    • Author(s)
      Okabe, S
    • Journal Title

      J. Differential Equations

      Volume: 252 Pages: 5155-5184

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the existence of mean curvature flow with transport term2010

    • Author(s)
      C. Liu, N. Sato, Y. Tonegawa
    • Journal Title

      Interfaces and Free Boundaries

      Volume: 12 Issue: 2 Pages: 251-277

    • DOI

      10.4171/ifb/234

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the existence of mean curvature flow with transport term2010

    • Author(s)
      Chun Liu
    • Journal Title

      Interfaces and Free Boundaries

      Volume: 12, no.2 Pages: 251-277

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 一般化された極小曲面や平均曲率流の正 則性理論について2013

    • Author(s)
      利根川吉廣
    • Organizer
      日本数学会年会総合講演
    • Place of Presentation
      京都大学(京都市)
    • Year and Date
      2013-03-21
    • Related Report
      2012 Final Research Report
  • [Presentation] A local regularity theorem on varifoldmean curvature flow2012

    • Author(s)
      利根川吉廣
    • Organizer
      NLPDEセミナー
    • Place of Presentation
      京都大学(京都市)
    • Year and Date
      2012-12-21
    • Related Report
      2012 Final Research Report
  • [Presentation] Almost everywhere regularity for weak mean curvature flow2012

    • Author(s)
      利根川吉廣
    • Organizer
      Tohoku University nonlinear PDE workshop
    • Place of Presentation
      29東北大学(仙台市)
    • Year and Date
      2012-09-28
    • Related Report
      2012 Final Research Report
  • [Presentation] Local regularity results on mean curvature flow2012

    • Author(s)
      利根川吉廣
    • Organizer
      ERC Workshop on Geometric PDEs
    • Place of Presentation
      Univ. of Pisa (Italy)
    • Year and Date
      2012-09-12
    • Related Report
      2012 Final Research Report
  • [Presentation] A local regularity theorem for weak mean curvature flow2012

    • Author(s)
      利根川吉廣
    • Organizer
      Conference `Geometric measure theory'
    • Place of Presentation
      Max Planck研究所 Golm (Germany)
    • Year and Date
      2012-07-02
    • Related Report
      2012 Final Research Report
  • [Presentation] Existence and regularity of mean curvature flow via Allen-Cahn equation2012

    • Author(s)
      利根川吉廣
    • Organizer
      12th International Conference on Free Boundary Problems: Theory and Applications
    • Place of Presentation
      Lake Chiemsee (Germany)
    • Year and Date
      2012-06-15
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] 平均曲率流の弱解に対する正則性理論2012

    • Author(s)
      利根川吉廣
    • Organizer
      日本数学会分科会一般講演
    • Place of Presentation
      東京理科大学(東京都)
    • Year and Date
      2012-03-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Brakke Type regularity2012

    • Author(s)
      利根川吉廣
    • Organizer
      Seminar
    • Place of Presentation
      Courant Institute (USA)
    • Year and Date
      2012-03-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Overview of generalized mean curvature flow2012

    • Author(s)
      利根川吉廣
    • Organizer
      Seminario de Analisis y geometria
    • Place of Presentation
      Univ Autonoma de Madrid (Spain)
    • Year and Date
      2012-02-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Overview of generalized mean curvature flow2012

    • Author(s)
      利根川吉廣
    • Organizer
      Conferencia del Departamento de Matematica Aplicada y el IMI
    • Place of Presentation
      Complutense Univ (Spain)
    • Year and Date
      2012-02-08
    • Related Report
      2012 Final Research Report
  • [Presentation] A general regularity theorem for weak mean curvature flow2012

    • Author(s)
      利根川吉廣
    • Organizer
      29th Kyushu Symposium on PDE
    • Place of Presentation
      九州大学(博多市)
    • Year and Date
      2012-01-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Almost everywhere regularity for weak mean curvature flow I, II, III2012

    • Author(s)
      利根川吉廣
    • Organizer
      Tohoku University nonlinear PDE workshop
    • Place of Presentation
      東北大学(仙台市)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] A new reglarity theorem for weak mean curvature flow2011

    • Author(s)
      利根川吉廣
    • Organizer
      8th East Asia Conference on PDE
    • Place of Presentation
      Pohang Univ, (Korea)
    • Year and Date
      2011-12-20
    • Related Report
      2012 Final Research Report
  • [Presentation] On the local regularity theorem for weak mean curvature flow2011

    • Author(s)
      利根川吉廣
    • Organizer
      Sino-Japan Conf. of Young Mathematicians
    • Place of Presentation
      Nankai Institute (China)
    • Year and Date
      2011-12-06
    • Related Report
      2012 Final Research Report
  • [Presentation] A general regularity theorem for weak mean curvature flow2011

    • Author(s)
      利根川吉廣
    • Organizer
      SNU-HU Joint Symposium in Mathematics
    • Place of Presentation
      Seoul National Univ, (Korea)
    • Year and Date
      2011-11-16
    • Related Report
      2012 Final Research Report
  • [Presentation] 平均曲率流の弱解とその正則性理論2011

    • Author(s)
      利根川吉廣
    • Organizer
      談話会
    • Place of Presentation
      東京理科大学(野田市)
    • Year and Date
      2011-11-01
    • Related Report
      2012 Final Research Report
  • [Presentation] A general regularity theorem for weak mean curvature flow2011

    • Author(s)
      利根川吉廣
    • Organizer
      第一回室蘭非線形解析セミナー
    • Place of Presentation
      29室蘭工業大学(室蘭市)
    • Year and Date
      2011-10-28
    • Related Report
      2012 Final Research Report
  • [Presentation] 平均曲率流の弱解についての新展開2011

    • Author(s)
      利根川吉廣
    • Organizer
      語ろう数理解析
    • Place of Presentation
      北海道大学(札幌市)
    • Year and Date
      2011-09-05
    • Related Report
      2012 Final Research Report
  • [Presentation] A new proof of Brakke's partial regularity for MCF2011

    • Author(s)
      利根川吉廣
    • Organizer
      PDE Workshop
    • Place of Presentation
      Oberwolfach研究所(Germany)
    • Year and Date
      2011-08-11
    • Related Report
      2012 Final Research Report
  • [Presentation] A new proof of Brakke's partial regularity for MCF2011

    • Author(s)
      利根川吉廣
    • Organizer
      Partial differential equations
    • Place of Presentation
      Oberwolfach (Germany)(招待講演)
    • Year and Date
      2011-08-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] Recent progress on stable minimal surface and its application2011

    • Author(s)
      利根川吉廣
    • Organizer
      Workshop on geometric analysis
    • Place of Presentation
      東北大学(仙台市)
    • Year and Date
      2011-02-22
    • Related Report
      2012 Final Research Report
  • [Presentation] Stable and unstable critical points of double-well energy2011

    • Author(s)
      利根川吉廣
    • Organizer
      第12回北東数学解析研究会
    • Place of Presentation
      東北大学(仙台市)
    • Year and Date
      2011-02-21
    • Related Report
      2012 Final Research Report
  • [Presentation] Two-phase flow problem with interfacial energy interaction2011

    • Author(s)
      利根川吉廣
    • Organizer
      Phase Field Models in Fluid Mechanics
    • Place of Presentation
      Univ. of Regensburg (Germany)
    • Year and Date
      2011-02-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Two-phase flow problem with interfacial energy interaction2011

    • Author(s)
      利根川吉廣
    • Organizer
      Phase Field Models in Fluid Mechanics
    • Place of Presentation
      Regensburg University(ドイツ、レーゲンスブルグ) 招待講演
    • Year and Date
      2011-02-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] 移流項をもつ平均曲率流の問題2010

    • Author(s)
      利根川吉廣
    • Organizer
      愛媛解析セミナー
    • Place of Presentation
      愛媛大学(松山市)
    • Year and Date
      2010-12-10
    • Related Report
      2012 Final Research Report
  • [Presentation] Regularity of stable diffuse interface2010

    • Author(s)
      利根川吉廣
    • Organizer
      応用解析研究会
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2010-11-13
    • Related Report
      2012 Final Research Report
  • [Presentation] 安定的な相分離面の正則性について2010

    • Author(s)
      利根川吉廣
    • Organizer
      日本数学会秋季総合分科会一般講演
    • Place of Presentation
      名古屋大学(名古屋市)
    • Year and Date
      2010-09-24
    • Related Report
      2012 Final Research Report
  • [Presentation] 安定的な相分離面の正則性について2010

    • Author(s)
      利根川吉廣
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Regularity of stable phase interfaces in the van der Waals-Cahn-Hilliard theory2010

    • Author(s)
      利根川吉廣
    • Organizer
      Recent Advances on de Giorgi's Conjecture and the Study of Entire Solutions of Nonlinear Scalar Equations
    • Place of Presentation
      BIRS, Banff (Canada)
    • Year and Date
      2010-08-12
    • Related Report
      2012 Final Research Report
  • [Presentation] Regularity of stable phase interfaces in the van der Waals-Cahn-Hilliard theory2010

    • Author(s)
      利根川吉廣
    • Organizer
      Recent Advances on de Giorgi's Conjecture and the Study of Entire Solutions of Nonlinear Scalar Equations
    • Place of Presentation
      Banff Inter'l Research Station(カナダ、バンプ) 招待講演
    • Year and Date
      2010-08-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the time-global existence for non-Newtonian two-phase flow with different densities2010

    • Author(s)
      利根川吉廣
    • Organizer
      Mathematical analysis on fluid and gas
    • Place of Presentation
      京大数理研(京都市)
    • Year and Date
      2010-07-09
    • Related Report
      2012 Final Research Report
  • [Presentation] 相分離界面と極小曲面の正則性理論について2010

    • Author(s)
      利根川吉廣
    • Organizer
      談話会
    • Place of Presentation
      神戸大学(神戸市)
    • Year and Date
      2010-06-16
    • Related Report
      2012 Final Research Report
  • [Presentation] A new two-phase fluid problem with surface energy2010

    • Author(s)
      利根川吉廣
    • Organizer
      New Trends in the Geometric Flow
    • Place of Presentation
      京大数理研(京都市)
    • Year and Date
      2010-06-08
    • Related Report
      2012 Final Research Report
  • [Presentation] On the regularity of stable phase interfaces2010

    • Author(s)
      利根川吉廣
    • Organizer
      HMA seminar
    • Place of Presentation
      広島大学(東広島市)
    • Year and Date
      2010-05-21
    • Related Report
      2012 Final Research Report
  • [Presentation] Analysis of two-phase problem: implications of phase field method to approximation scheme2010

    • Author(s)
      利根川吉廣
    • Organizer
      HMC Seminar
    • Place of Presentation
      金沢大学(金沢市)
    • Year and Date
      2010-03-17
    • Related Report
      2012 Final Research Report
  • [Presentation] フェイズフィールド法にまつわる変分問題(2回連続講演)2010

    • Author(s)
      利根川吉廣
    • Organizer
      Workshop 「変分法と領域摂動」
    • Place of Presentation
      神戸インスティチュート(神戸市)
    • Related Report
      2012 Final Research Report
  • [Presentation] フェイズフィールド法にまつわる変分問題2010

    • Author(s)
      利根川吉廣
    • Organizer
      ワークショップ「領域摂動と変分法」
    • Place of Presentation
      神戸インスティチュート
    • Related Report
      2009 Annual Research Report
  • [Presentation] Existence of weak mean curvature flow with non-smooth forcing term2009

    • Author(s)
      利根川吉廣
    • Organizer
      SIAM conference on Analysis of PDEs
    • Place of Presentation
      Hilton Miami Downtown (USA)
    • Year and Date
      2009-12-07
    • Related Report
      2012 Final Research Report
  • [Presentation] Existence of weak mean curvature flow with non-smooth forcing term2009

    • Author(s)
      利根川吉廣
    • Organizer
      SIAM conference on Analysis of PDEs
    • Place of Presentation
      米国マイアミ市
    • Year and Date
      2009-12-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] 表面張力と移流効果の動的なせめぎあい2009

    • Author(s)
      利根川吉廣
    • Organizer
      談話会
    • Place of Presentation
      東北大学(仙台市)
    • Year and Date
      2009-10-26
    • Related Report
      2012 Final Research Report
  • [Presentation] Existence of mean curvature flow with non-smooth transport term2009

    • Author(s)
      利根川吉廣
    • Organizer
      PDE Workshop
    • Place of Presentation
      Oberwolfach 研究所 (Germany)
    • Year and Date
      2009-08-07
    • Related Report
      2012 Final Research Report
  • [Presentation] Existence of mean curvature flow with non-smooth transport term2009

    • Author(s)
      利根川吉廣
    • Organizer
      Workshop 'Partielle Differentialgleichungen'
    • Place of Presentation
      ドイツOberwolfach研究所
    • Year and Date
      2009-08-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] Existence of mean curvature flow with non-smooth transport term2009

    • Author(s)
      利根川吉廣
    • Organizer
      PIMS workshop, Asymptotic analysis in the calculus of variations and PDEs
    • Place of Presentation
      Univ. of British Columbia (Canada)
    • Year and Date
      2009-07-07
    • Related Report
      2012 Final Research Report
  • [Presentation] Existence of mean curvature flow with non-smooth transport term2009

    • Author(s)
      利根川吉廣
    • Organizer
      PIMS workshop, Asymptotic analysis in the calculus of variations and PDEs
    • Place of Presentation
      カナダ ブリティッシュコロンビア大学
    • Year and Date
      2009-07-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] Variational problems motivated by large deviation theory2009

    • Author(s)
      利根川吉廣
    • Organizer
      微分方程式セミナー
    • Place of Presentation
      大阪大学(大阪市)
    • Year and Date
      2009-06-05
    • Related Report
      2012 Final Research Report
  • [Presentation] A local regularity theorem for weak mean curvature flow

    • Author(s)
      利根川吉廣
    • Organizer
      Conference `Geometric measure theory'
    • Place of Presentation
      Max Planck Institute Golm (Germany)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Local regularity results on mean curvature flow

    • Author(s)
      利根川吉廣
    • Organizer
      ERC Workshop on Geometric PDEs
    • Place of Presentation
      University of Pisa (Italy)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] A local regularity theorem on varifold mean curvature flow

    • Author(s)
      利根川吉廣
    • Organizer
      NLPDE seminar
    • Place of Presentation
      京都大学(京都市)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 一般化された極小曲面や平均曲率流の正則性理論について

    • Author(s)
      利根川吉廣
    • Organizer
      日本数学会2013年度年会総合講演
    • Place of Presentation
      京都大学(京都市)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Remarks]

    • URL

      http://www.math.sci.hokudai.ac.jp/~tonegawa/toppagejp.htm

    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://www.math.sci.hokudai.ac.jp/~tonegawa/toppagejp.htm

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.sci.hokudai.ac.jp/~tonegawa/toppagejp.htm

    • Related Report
      2010 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi