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2009 Fiscal Year Final Research Report

New topics for partial differential equations whose solution has singular sets

Research Project

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Project/Area Number 18340047
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

OMATA Seiro  Kanazawa University, 数物科学系, 教授 (20214223)

Co-Investigator(Kenkyū-buntansha) MIYAKAWA Tetsuro  金沢大学, 自然科学研究科, 教授 (10033929)
JINBO Shuichi  北海道大学, 理学系研究院, 教授 (80201565)
KIKUCHI Koji  静岡大学, 工学部, 教授 (50195202)
WEISS Georg  東京大学, 数理科学研究院, 准教授 (30282817)
YAMAURA Yoshihiko  日本大学, 文理学部, 教授 (90255597)
Co-Investigator(Renkei-kenkyūsha) KOBAYASHI Kenta  金沢大学, 数物科学系, 准教授 (60432902)
NAGAYAMA Masaharu  金沢大学, 数物科学系, 教授 (20314289)
Project Period (FY) 2006 – 2009
Keywords変分問題 / 特異点 / 数値解析 / 自由境界 / 離散勾配流
Research Abstract

時間発展の偏微分方程式で解に特異点が生じる問題群についての数学的解析と数値解法の開発を行ってきた。特に双曲型体積保存自由境界問題・放物型体積保存自由境界問題では解の存在と一意性について一定の結果を得た。すなわち、新しい弱解定義、構成、放物型については、弱解のヘルダー連続性を示した。また、数値解法についても、ラグランジェアンの停留点を求める方法論としての離散勾配流法の有効性を確かめるとともに、これを用いた連成解析用のソルバーを開発した。さらに、一部ソバーについては並列化を行いパラレルマシン対応とした。

  • Research Products

    (19 results)

All 2009 2008 2007 2006 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (11 results) Remarks (1 results)

  • [Journal Article] Mathematical analysis of a constrained parabolic free boundary problem describing droplet motion on a surface2009

    • Author(s)
      K. Svadlenka, S. Omata
    • Journal Title

      Indiana University Mathematics Journa l58(5)

      Pages: 2073-2102

    • Peer Reviewed
  • [Journal Article] Variational approach to evolutionary free boundary problems2009

    • Author(s)
      S. Omata, M. Kazama, H. Nakagawa
    • Journal Title

      Nonlinear Analysis 71

      Pages: e1547-e1552

    • Peer Reviewed
  • [Journal Article] Modeling and computation of fluid-membrane interaction2009

    • Author(s)
      M. Kazama, S. Omata
    • Journal Title

      Nonlinear Analysis 71

      Pages: e1553-e1559

    • Peer Reviewed
  • [Journal Article] Construction of weak solution to hyperbolic problem with volume constraint2008

    • Author(s)
      K. Svadlenka, S. Omata
    • Journal Title

      Nonlinear Analysis 69

      Pages: 3202-3212

    • Peer Reviewed
  • [Journal Article] Construction of solutions to heat type problems with volume constraint via the discrete Morse flow2007

    • Author(s)
      K. Svadlenka, S. Omata
    • Journal Title

      Funkcialaj Ekvacioj

      Pages: ee50261-285

    • Peer Reviewed
  • [Journal Article] Numerical solution of film vibration with obstacle Adv.2006

    • Author(s)
      H. Yoshiuchi, S. Omata, K. Svadlenka, K. Ohara
    • Journal Title

      Math. Sci. Appl. 16,1

      Pages: 33-43

    • Peer Reviewed
  • [Journal Article] Construction of approximate solution to a hyperbolic free boundary problem with volume constraint and its numerical computation2006

    • Author(s)
      T. Yamazaki, S. Omata, K. Svadlenka, K. Ohara
    • Journal Title

      Adv. Math. Sci. Appl. 16,1

      Pages: 57-67

    • Peer Reviewed
  • [Presentation] 付着・剥離・衝突現象の数理解析2009

    • Author(s)
      小俣正朗
    • Organizer
      日本数学会秋期総合分科会特別講演
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-26
  • [Presentation] Mathematical Theory and Numerical Calculations of Collision2008

    • Author(s)
      S. Omata
    • Organizer
      Peeling and Attached Droplets, Invited Plenary Talk in The Second International Conference on Mathematics and Natural Sciences
    • Place of Presentation
      Bandung Indonesia
    • Year and Date
      2008-10-29
  • [Presentation] Mathematical theory and numerical calculations of collision, peeling and attached droplets2008

    • Author(s)
      S. Omata
    • Organizer
      Invited Speaker in The Second China-Japan-Korea Workshop on Numerical Mathematics Weihai
    • Place of Presentation
      Shandong Province
    • Year and Date
      2008-08-26
  • [Presentation] Variational approach to evolutionary free boundary problems2008

    • Author(s)
      S. Omata
    • Organizer
      Keynote speaker(Invited Prenary talk) in World Congress of Nonlinear Analysis 2008 at Florida
    • Year and Date
      2008-07-04
  • [Presentation] Discrete Morse flow for nonlocal problems2008

    • Author(s)
      小俣正朗
    • Organizer
      変分問題とその周辺京都大学数理解析研究所
    • Year and Date
      2008-06-24
  • [Presentation] Motion of water droplets in contact with a surface2008

    • Author(s)
      S. Omata
    • Organizer
      Ryukoku Workshop 2008 : Recent Progress on Pattern Formation and Dynamics in Mathematical Sciences
    • Place of Presentation
      龍谷大学
    • Year and Date
      2008-06-13
  • [Presentation] Droplet Motion on a plane International Conference on Computational Science2007

    • Author(s)
      S. Omata
    • Organizer
      International Conference on Computational Science
    • Place of Presentation
      Bandung Invited Talk
    • Year and Date
      2007-12-03
  • [Presentation] Droplet Motion on a plane Equadiff 07 5th- 11th Augsut 2007, (Wien)2007

    • Author(s)
      S. Omata
    • Year and Date
      2007-08-10
  • [Presentation] Droplet motion with some contact angle Czech-Japanese Seminar in Applied Mathematics 20062006

    • Author(s)
      S. Omata
    • Organizer
      FNSPE CTU in Prague & Institute of Thermomechanics of the Czech Academy of Sciences
    • Place of Presentation
      Department of Mathematics
    • Year and Date
      20060914-20061916
  • [Presentation] Bubble Motion on Water Surface HK-Japan Workshop on Pattern Formations and Reaction-Diffusion Systems2006

    • Author(s)
      S. Omata
    • Organizer
      Institute of Math. Chinese U. of HongKong Invited Talk
    • Year and Date
      2006-12-15
  • [Presentation] On a hyperbolic free boundary problem First Slovak-Japan workshop on Computational Mathematics2006

    • Author(s)
      S. Omata
    • Place of Presentation
      ブラチスラバ
    • Year and Date
      2006-09-10
  • [Remarks]

    • URL

      http://polaris.s.kanazawa-u.ac.jp/

URL: 

Published: 2011-06-18   Modified: 2016-04-21  

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