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On the asymptotics and well-posedness for Keller-Segel system of degenerate and singular type

Research Project

Project/Area Number 15K04961
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research InstitutionOsaka University (2018)
Kyushu University (2015-2017)

Principal Investigator

Sugiyama Yoshie  大阪大学, 情報科学研究科, 教授 (60308210)

Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords退化放物型方程式 / Keller-Segel系 / 漸近解析 / 非自明定常解 / 退化型 / 閾値 / 定常解 / 有限伝播性 / Navier-Stokes方程式 / 退化放物型 / 特異放物型 / 初期値問題の時間局所適切性 / 爆発解 / Keller-Segel 系 / chemotaxis / well-posedness / Navier-Stokes 方程式 / Uniqueness
Outline of Final Research Achievements

We investigated asymptotic analysis at infinite time with the degenerate Keller-Segel system. More precisely, we proved the existence of nontrivial stationary solutions of the Keller-Segel system, and further proved the fact that the profiles for the Keller-Segel system, which are time-evolving solutions, have the same stationary solution at time infinity. The research results have been published in IUMJ in 2018 as a joint research with Mr. Jose Carrillo.

Academic Significance and Societal Importance of the Research Achievements

退化楕円型方程式の変分問題を解くことに帰着し,Keller-Segel系の非自明な定常解の存在証明を確立している.同問題の解析には,退化性が誘引する正則性欠如を克服する必要がある.我々は,球対称性を担保することで解のサポートコンパクト性を保証し,解析を容易にする手法を確立している.同手法は多様な退化型方程式系の解析に有効である.

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (30 results)

All 2018 2017 2016 2015 Other

All Int'l Joint Research (3 results) Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 4 results) Presentation (22 results) (of which Int'l Joint Research: 10 results,  Invited: 19 results)

  • [Int'l Joint Research] Imperial College London(英国)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Seoul National University(韓国)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Yonsei University(韓国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Compactly supported stationary states of the degenerate Keller-Segel system in the diffusiondominated regime2018

    • Author(s)
      J.Carrillo and Y.Sugiyama
    • Journal Title

      Indiana Univ. Math. J.

      Volume: 67

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid2016

    • Author(s)
      H.Kozono, M.Miura and Y.Suiyama
    • Journal Title

      J. Funct. Anal.

      Volume: 270 Pages: 1663-1683

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Uniqueness theorem on weak solutions to the Keller-Segel system of degenerate and singular types2016

    • Author(s)
      T.Kawakami and Y.Sugiyama
    • Journal Title

      J. Differential Equations

      Volume: 260 Pages: 4683-4716

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness theorem on mild solutions to the Keller–Segel system coupled with the Navier–Stokes fluid2016

    • Author(s)
      H.Kozono; M.Miurai; Y.Sugiyama
    • Journal Title

      J. Funct. Anal.

      Volume: 270 Issue: 5 Pages: 1663-1683

    • DOI

      10.1016/j.jfa.2015.10.016

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Uniqueness theorem on weak solutions to the Keller-Segel system of degenerate and singular types2016

    • Author(s)
      T.Kawakami; Y.Sugiyama
    • Journal Title

      J. Differential Equations

      Volume: 260 Issue: 5 Pages: 4683-4716

    • DOI

      10.1016/j.jde.2015.11.021

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] 脳動脈瘤治癒過程における血栓化ダイナミクスを説明する数理モデルの構築2018

    • Author(s)
      杉山由恵
    • Organizer
      CREST・さきがけ・AIMaP合同シンポジウム「数学パワーが世界を変える2019」
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On the ε-regularity theorem for the Keller-Segel systems and its application to the analysis of singular sets2018

    • Author(s)
      杉山由恵
    • Organizer
      京都大学NLPDEセミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Measure valued solutions of 2D Keller-Segel systems2018

    • Author(s)
      杉山由恵
    • Organizer
      The 16th Linear and Nonlinear Waves
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Measure valued solutions of 3D Keller-Segel systems2018

    • Author(s)
      杉山由恵
    • Organizer
      RIMS 研究集会 「反応拡散方程式‐伝播現象と特異性の解析および諸科科学への応用」
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Compactly supported stationary states of the degenerate Keller-Segel system in the difusion-dominated regime2018

    • Author(s)
      杉山由恵
    • Organizer
      2018年度偏微分方程式 集中セミナープログラム
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On the Structure of Solutions of Keller-Segel Systems with Sinks of Fluid2018

    • Author(s)
      杉山由恵
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, SS10
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Compactly supported stationary states of the degenerate Keller-Segel systemin the difusion-dominated regime2018

    • Author(s)
      杉山由恵
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, SS11
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 退化型Keller-Segel系の解構造について2018

    • Author(s)
      杉山由恵
    • Organizer
      大阪大学数学科談話会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On the structure of solutions of Keller-Segel systems with fluid and its application to life science2018

    • Author(s)
      杉山由恵
    • Organizer
      大阪大学 微分方程式セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Compactly supported stationary states of the degenerate Keller-Segel systemin the difusion-dominated regime2018

    • Author(s)
      杉山由恵
    • Organizer
      南大阪応用数学セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Global existence and finite time blow-up criterion of solutions to the Keller-Segel systems coupled with the Navier-Stokes fluid2017

    • Author(s)
      Yoshie Sugiyama
    • Organizer
      Tianfu International Conference on PDEs
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Global existence and finite time blow-up criterion of solutions to the Keller-Segel systems coupled with the Navier-Stokes fluid2017

    • Author(s)
      Yoshie Sugiyama
    • Organizer
      KWMS(Korean Women in Mathematical Sciences) International Conference
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the structure of solutions of Keller-Segel systems with sinks of fluid2017

    • Author(s)
      Yoshie Sugiyama
    • Organizer
      第8回 拡散と移流の数理
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] On the structure of solutions of Keller-Segel systems with sinks of fluid2017

    • Author(s)
      Yoshie Sugiyama
    • Organizer
      The 3rd International Workshop on Mathematical Analysis of Chemotaxis
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid2017

    • Author(s)
      三浦正成
    • Organizer
      日本数学会
    • Place of Presentation
      首都大学東京
    • Related Report
      2016 Research-status Report
  • [Presentation] On H¨older continuity of solutions to fast diffusion equations with external forces and its applications2017

    • Author(s)
      杉山由恵
    • Organizer
      The second international workshop on mathematical analysis of chemotaxis
    • Place of Presentation
      東京理科大学
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Time global existence and finite time blow-up criterion for solutions to the Keller-Segel system coupled with Navier-Stokes fluid2016

    • Author(s)
      杉山由恵
    • Organizer
      International Workshop on Mathematical Analysis of Chemotaxis
    • Place of Presentation
      東京理科大学
    • Year and Date
      2016-02-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Time global existence and finite time blow-up criterion for solutions to the Keller-Segel system coupled with Navier-Stokes fluid2016

    • Author(s)
      杉山由恵
    • Organizer
      北陸応用数理研究会2016 金沢大学
    • Place of Presentation
      金沢大学
    • Year and Date
      2016-02-17
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Global existence and finite time blow-up criterion of solutions to the Keller-Segel systems coupled with the Navier-Stokes fluid2016

    • Author(s)
      杉山由恵
    • Organizer
      Workshop on Nonlinear Partial Differential Equations -China-Japan Joint Project for Young Mathematicians 2016
    • Place of Presentation
      East China Normal University, Shanghai
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Global existence and finite time blow-up criterion of solutions to the Keller-Segel systems coupled with the Navier-Stokes fluid2016

    • Author(s)
      杉山由恵
    • Organizer
      Interactions between Partial Differential Equations & Functional Inequalities
    • Place of Presentation
      Intstitute Mittag-Leffler, Sweden
    • Related Report
      2016 Research-status Report
  • [Presentation] Global existence and finite time blow-up criterion of solutions to the Keller-Segel systems coupled with the Navier-Stokes fluid2016

    • Author(s)
      杉山由恵
    • Organizer
      7th Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      The Mathematical Research and Conference Center, Poland
    • Related Report
      2016 Research-status Report
  • [Presentation] Mathematical Modeling and Analysis of Chemotactic Cell Migration2015

    • Author(s)
      杉山由恵
    • Organizer
      京都大学 生命動態システム科学拠点セミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2015-11-06
    • Related Report
      2015 Research-status Report
    • Invited

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Published: 2015-04-16   Modified: 2022-02-03  

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