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Compact traveling waves for mean-curvature flow with driving force

Research Project

Project/Area Number 18K13458
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionOkayama University

Principal Investigator

MONOBE HARUNORI  岡山大学, 異分野基礎科学研究所, 特任准教授 (20635809)

Project Period (FY) 2018-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords平均曲率流方程式 / 進行波解 / 界面方程式
Outline of Final Research Achievements

We studied the mean-curvature flow with driving force which is derived from some mathematical models, such as cell-locomotion and droplet motion. As a result, we have the following results : (1) if the driving force is positive, there exists a unique compact traveling wave (CTW) solutions. (2) if the driving force is negative, there does not exists any CTW solutions. (3). if the driving force is sign-changing and some conditions are satisfied, there exists a unique CTW solutions. (4). if CTW exists, every CTW is convex and unstable.

Academic Significance and Societal Importance of the Research Achievements

偏微分方程式で記述される数理モデルにおいて、スポット状パターンの発生メカニズムは未だ明確にはわかっておらず、現在もモデル構築の際は、経験則に頼るところが多い。このため、より複雑な形状のパターンへの解析が滞っている。本研究成果は、スポット状の物質が移動する現象の数理モデルを考えた時に、その構築方法や解の振る舞いの解析の手助けになると考えられる。

Report

(5 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (28 results)

All 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (3 results) Journal Article (5 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 5 results) Presentation (20 results) (of which Int'l Joint Research: 11 results,  Invited: 17 results)

  • [Int'l Joint Research] University of Wyoming(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] National Chiao Tung University(その他の国・地域)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] 国立台南大学(その他の国・地域)

    • Related Report
      2018 Research-status Report
  • [Journal Article] Convergence to a traveling wave in the logarithmic diffusion equation with a bistable nonlinearity2022

    • Author(s)
      Hiroshi Matsuzawa, Harunori Monobe, Masahiko Shimojo, Eiji Yanagida
    • Journal Title

      Indiana University Mathematics Journal

      Volume: 1 Pages: 125-151

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact traveling waves for anisotropic curvature flows with driving force2021

    • Author(s)
      Harunori Monobe, Hirokazu Ninomiya
    • Journal Title

      Transactions of The American Mathematical Society

      Volume: 20 Issue: 4 Pages: 2447-2477

    • DOI

      10.1090/tran/8168

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] The formation of spreading front : the singular limit of three-component reaction-diffusion models2021

    • Author(s)
      Hirofumi Izuhara, Harunori Monobe, Chang-Hong Wu,
    • Journal Title

      Journal of Mathematical Biology

      Volume: 82 Issue: 5 Pages: 1-33

    • DOI

      10.1007/s00285-021-01591-5

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] V-shaped fronts around an obstacle2020

    • Author(s)
      H. Guo and H. Monobe
    • Journal Title

      Mathematische Annalen

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Compact traveling wave for anisotropic curvature flow with driving force2020

    • Author(s)
      H. Monobe and H. Ninomiya
    • Journal Title

      Transaction of the American Mathematical Society

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] 結晶粒界溝の成長に関連する界面方程式の解の挙動2021

    • Author(s)
      物部治徳
    • Organizer
      楕円型・放物型微分方程式研究集会
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Fisher-Stefan モデルの反応拡散系近似とその周辺について2021

    • Author(s)
      物部治徳
    • Organizer
      神戸解析セミナー
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Singular limit of a mathematical model related to controlling invasive alien species2021

    • Author(s)
      Harunori Monobe
    • Organizer
      Society for Mathematical Biology 2021
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Fisher-Stefan problems and the singular limit of reaction-diffusion systems2021

    • Author(s)
      Harunori Monobe
    • Organizer
      Czech-Japanese Seminar in Applied Mathematics
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Fisher-KPP model and Fast reaction limits of RDs2021

    • Author(s)
      物部治徳
    • Organizer
      京都駅前セミナー
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Fast reaction limit of three-components reaction-diffusion systems and free boundary problems describing population dynamics2020

    • Author(s)
      Harunori Monobe
    • Organizer
      Interfacial Phenomena in Reaction-Diffusion Systems
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Fast reaction limit of a three-components Lotka-Volterra competition-diffusion system2020

    • Author(s)
      Harunori Monobe
    • Organizer
      ``An online conference on mathematical biology'' ReaDiNet
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Behaviour of solutions to an interface equation with exponential curvature2019

    • Author(s)
      Harunori Monobe
    • Organizer
      2019 International Workshop on PDEs and Applications
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On a fully nonlinear parabolic equation related to a groove profile in crystal grain regions2019

    • Author(s)
      Harunori Monobe
    • Organizer
      Qualitative Theory on Nonlinear Partial Differential Equation
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the behaviour of solutions to an exponential type curvature equation2019

    • Author(s)
      Harunori Monobe
    • Organizer
      ICIAM 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On a fully nonlinear parabolic equation with prescribed contact angle2019

    • Author(s)
      Harunori Monobe
    • Organizer
      Mini-workshop on Nonlinear Diffusion problems
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On compact traveling wave for a mean-curvature flow with driving force2019

    • Author(s)
      Harunori Monobe
    • Organizer
      2019 SIAM Conference on Dynamical Systems
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 指数型非線形性を持つ曲率依存方程式の解の挙動について2019

    • Author(s)
      物部治徳
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] 個体群動態に関連する移流項を伴う自由境界問題の解析2019

    • Author(s)
      物部治徳
    • Organizer
      第2回はこだて現象数理研究集会
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 外力を持つ平均曲率流方程式の進行波解の存在2019

    • Author(s)
      物部治徳
    • Organizer
      非線形問題への常微分方程式の手 法によるアプローチ
    • Related Report
      2018 Research-status Report
  • [Presentation] Compact traveling waves for a curvature flow with driving force2018

    • Author(s)
      Harunori Monobe
    • Organizer
      2018 China-Japan Workshop on Nonlinear Diffusion Problems
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Compact traveling wave solutions to curvature flows with a driving force in R^32018

    • Author(s)
      Harunori Monobe
    • Organizer
      The 12th AIMS Conference on Dynamical Systems
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 外力付き平均曲率流方程式のコンパクトな進行波解2018

    • Author(s)
      物部治徳
    • Organizer
      なかもず解析セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] 外力付き平均曲率流方程式のコンパクトな進行波解について2018

    • Author(s)
      物部治徳
    • Organizer
      HMMC セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 外力を持つ平均曲率方程式のコンパクトな進行波解2018

    • Author(s)
      物部治徳
    • Organizer
      松江セミナー
    • Related Report
      2018 Research-status Report
    • Invited

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Published: 2018-04-23   Modified: 2023-01-30  

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