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Investigations on solution structures of generalized chemotaxis systems

Research Project

Project/Area Number 17H07131
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Mathematical analysis
Research InstitutionTokyo University of Science

Principal Investigator

Fujie Kentaro  東京理科大学, 理学部第一部数学科, 助教 (50805398)

Research Collaborator Senba Takasi  
Cieslak Tomasz  
Project Period (FY) 2017-08-25 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords走化性方程式 / Keller-Segel系 / 放物型方程式 / 関数方程式 / 爆発現象 / 走化性 / オイラー方程式
Outline of Final Research Achievements

In this research I consider behaviors of solutions to generalized problems of the chemotaxis system, which describes a movement of cells induced by chemotaxis. I classified behaviors of solutions to the chemotaxis system with generalized sensitivity functions by decaying rates of sensitivity functions. Technically, we introduced a new viewpoint of regarding the chemotaxis system as a perturbation of a single equation and estimating perturbation errors. Moreover, we focused on mathematical structures of chemotaxis systems and study behaviors of solutions to some system, which is a generalization of chemotaxis systems from a structural viewpoint. Especially, we showed that a mass critical phenomenon occurs in the four-dimensional setting.

Academic Significance and Societal Importance of the Research Achievements

本研究の対象である走化性方程式系は、がん浸潤現象をはじめとする多くの生物現象を記述する数理モデルの基礎方程式である。そのため、走化性方程式系の解の挙動に関する研究は、走化性による粘菌の挙動(集中現象など)を解明する数学的解析としての意義がある。学術的には、複数の偏微分方程式による連立系には従来の多くの研究手法が使えず、国際的に研究活動が活発である。本研究では、連立系を単独方程式の摂動として扱うという新手法を開発し、また問題の持つ構造に視点を移して解の挙動を研究した。

Report

(3 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • Research Products

    (20 results)

All 2019 2018 2017 Other

All Int'l Joint Research (2 results) Journal Article (7 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 7 results) Presentation (10 results) (of which Int'l Joint Research: 6 results,  Invited: 10 results) Remarks (1 results)

  • [Int'l Joint Research] Polish Academy of Sciences(ポーランド)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Polish Academy of Sciences(ポーランド)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Blowup of solutions to a two-chemical substances chemotaxis system in the critical dimension2019

    • Author(s)
      Fujie Kentarou、Senba Takasi
    • Journal Title

      Journal of Differential Equations

      Volume: 266 Issue: 2-3 Pages: 942-976

    • DOI

      10.1016/j.jde.2018.07.068

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global existence and boundedness in a fully parabolic 2D attraction- repulsion system: chemotaxis-dominant case2019

    • Author(s)
      Fujie Kentarou、Suzuki Takashi
    • Journal Title

      ADVANCES IN MATHEMATICAL SCIENCES AND APPLICATIONS

      Volume: 28 Pages: 1-9

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boundedness of solutions to the critical fully parabolic quasilinear one‐dimensional Keller-Segel system2018

    • Author(s)
      Bieganowski Bartosz、Cieslak Tomasz、Fujie Kentarou、Senba Takasi
    • Journal Title

      Mathematische Nachrichten

      Volume: 292 Issue: 4 Pages: 724-732

    • DOI

      10.1002/mana.201800175

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Global existence in the 1D quasilinear parabolic-elliptic chemotaxis system with critical nonlinearity2018

    • Author(s)
      Cieslak Tomasz、Fujie Kentarou
    • Journal Title

      Discrete & Continuous Dynamical Systems - S

      Volume: 0 Issue: 2 Pages: 165-176

    • DOI

      10.3934/dcdss.2020009

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Global asymptotic stability in a chemotaxis-growth model for tumor invasion2018

    • Author(s)
      Fujie Kentarou
    • Journal Title

      Discrete & Continuous Dynamical Systems - S

      Volume: 0 Issue: 2 Pages: 203-209

    • DOI

      10.3934/dcdss.2020011

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] No critical nonlinear diffusion in 1D quasilinear fully parabolic chemotaxis system2018

    • Author(s)
      Cieslak Tomasz、Fujie Kentarou
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 146 Issue: 6 Pages: 2529-2540

    • DOI

      10.1090/proc/13939

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system2018

    • Author(s)
      Fujie Kentarou、Senba Takasi
    • Journal Title

      Nonlinearity

      Volume: 31 Issue: 4 Pages: 1639-1672

    • DOI

      10.1088/1361-6544/aaa2df

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] 感応性関数をもつ走化性方程式について2019

    • Author(s)
      藤江健太郎
    • Organizer
      第13回室蘭工業大学応用解析セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Global existence and boundedness in a fully parabolic two-chemical substances chemotaxis system2018

    • Author(s)
      Kentarou Fujie
    • Organizer
      8th Euro-Japanese Workshop on Blow-up
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] New Lyapunov-like functional of 1D quasilinear Keller-Segel system and its application2018

    • Author(s)
      Kentarou Fujie
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] No critical nonlinear diffusion in 1D quasilinear fully parabolic chemotaxis system2018

    • Author(s)
      Kentarou Fujie
    • Organizer
      Seminarium Zaklladu Rownan Fizyki Matematycznej
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 1 次元準線形 Keller-Segel 系の臨界現象の非存在性2018

    • Author(s)
      藤江健太郎
    • Organizer
      応用数学セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] A higher dimensional generalization of the Keller-Segel system2018

    • Author(s)
      Kentarou Fujie
    • Organizer
      Mathematical aspects of chemotaxis, cross-diffusion effects and concentration phenomena
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On an attraction-repulsion chemotaxis system2018

    • Author(s)
      Kentarou Fujie
    • Organizer
      The 3rd International Workshop on Mathematical Analysis of Chemotaxis
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] No critical nonlinear diffusion in 1D quasilinear fully parabolic Keller--Segel system2018

    • Author(s)
      Kentarou Fujie
    • Organizer
      第35回 九州における偏微分方程式研究集会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] A generalization of the Keller--Segel system to higher dimensions from a structural viewpoint2017

    • Author(s)
      Kentarou Fujie
    • Organizer
      Equadiff 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] No critical nonlinear diffusion in 1D quasilinear fully parabolic Keller--Segel system2017

    • Author(s)
      藤江健太郎
    • Organizer
      第7回室蘭非線形解析研究会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Remarks] 藤江 健太郎 | 教員紹介 | 東京理科大学 理学部第一部数学科

    • URL

      http://math-1.ma.kagu.tus.ac.jp/faculty-member/kentarou-fujie/

    • Related Report
      2017 Annual Research Report

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Published: 2017-08-25   Modified: 2020-03-30  

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