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On asymptotic behavior and interface curve of solution for Keller-Segel system of degenerate type

Research Project

Project/Area Number 21540197
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka City University (2011)
Tsuda College (2009-2010)

Principal Investigator

SUGIYAMA Yoshie  大阪市立大学, 大学院・理学研究科, 教授 (60308210)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords退化型 / Keller-Segel系 / 爆発解 / 測度値解 / 有限時間爆発 / 時間大域解 / 退化放物型方程式 / デルタ関数 / 退化型Keller-Segel系 / 界面曲線 / 有限伝播性 / 部分正則性定理
Research Abstract

Measure valued solution : The time global solution has been constructed for Keller-Segel system of semi-linear type by expanding the functional space to the measure valued solution.
Asymptotics : We have proved that the solution of Keller-Segel system behaves like a stationary solution asymptotically as time tends to infinity.
Uniqueness : We have established the functional space which the weak solution becomes unique.
Finite speed propagation : The existence of solution and the extinction phenomena has been proved for Keller-Segel system of singular type.

Report

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

    (57 results)

All 2012 2011 2010 2009 Other

All Journal Article (40 results) (of which Peer Reviewed: 40 results) Presentation (17 results)

  • [Journal Article] Measure valued solutions of the 2D Keller-Segel system2012

    • Author(s)
      S.Luckhaus, Y.Sugiyama, J.J.L.Velazquez
    • Journal Title

      Archive for Rational Mechanics and Analysis

      Volume: (掲載決定であるがページ数と巻号は未定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite speed of propagation in 1-D degenerate Keller-Segel system2012

    • Author(s)
      Y.Sugiyama
    • Journal Title

      Math.Nachr

      Volume: 285 Pages: 744-757

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness theorem of mild solutions to the Keller-Segel system in the scaling invariant space2012

    • Author(s)
      H.Kozono, Y.Sugiyama, T.Wachi
    • Journal Title

      J.Differential Equations

      Volume: 252 Pages: 1213-1228

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extinction and asymptotic behavior of solutions for the Keller-Segel system of fast diffusion type2011

    • Author(s)
      Y. Sugiyama and Y. Yahagi
    • Journal Title

      Adv. Math. Sci. Appl.

      Volume: 35 Pages: 209-219

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Extinction, decay and blow-up for Keller-Segel system of fast diffusion type2011

    • Author(s)
      Y. Sugiyama and Y. Yahagi
    • Journal Title

      J. Differential Equations

      Volume: 250 Pages: 3047-3087

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Self-similar blow-up with a continuo-us range of values of the aggregated mass for a degenerate Keller-Segel system2011

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

      Advances in Differential Equations

      Volume: 16 Pages: 85-112

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Extinction, decay and blow-up for Keller-Segel system of fast diffusion type2011

    • Author(s)
      Y.Sugiyama, Y.Yahagi
    • Journal Title

      J.Differential Equations

      Volume: 250 Pages: 3047-3087

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extinction and asymptotic behavior of solutions for the Keller-Segel system of fast diffusion type2011

    • Author(s)
      Y.Sugiyama, Y.Yahagi
    • Journal Title

      Adv.Math.Sci.Appl

      Volume: 35 Pages: 201-219

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Self-similar blow-up with a continuous range of values of the aggregated mass for a degenerate Keller-Segel system2011

    • Author(s)
      Y.Sugiyama, J.J.L.Velazquez
    • Journal Title

      Advances in Differential Equations

      Volume: 16 Pages: 85-112

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extinction, decay and blow-up for Keller-Segel system of fast diffusion type2011

    • Author(s)
      杉山由恵, 矢作由美
    • Journal Title

      J.Differential Equations

      Volume: (掲載確定 印刷中により未定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness and continuity of solution for the initial data in the scaling invariant class of degenerate Keller-Segel system2011

    • Author(s)
      杉山由恵, 矢作由美
    • Journal Title

      J.Evolution Equations

      Volume: (掲載確定 印刷中により未定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extinction and asymptotic behavior of solutions for the Keller-Segel system of fast diffusion type2011

    • Author(s)
      杉山由恵, 矢作由美
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: (掲載確定 印刷中により未定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite speed of propagation in 1-D degenerate Keller-Segel system2011

    • Author(s)
      杉山由恵
    • Journal Title

      Math.Nachr

      Volume: (掲載確定 印刷中により未定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Self similar blow up with different values of the masses for the Keller Segel system with nonlinear diffusion in the critical case2011

    • Author(s)
      杉山由恵, J.J.L.Velazquez
    • Journal Title

      Advances in Differential Equations

      Volume: 16 Pages: 85-112

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness and continuity of solution for the initial data in the scaling invariant class of degenerate Keller-Segel system2010

    • Author(s)
      Y. Sugiyama and Y. Yahagi
    • Journal Title

      J. Evol.Equ.

      Volume: 11 Pages: 319-337

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness and regularity of weak solutions for the1-D degenerate Keller-Segel systems Nonlinear Analysis Series A : Theory2010

    • Author(s)
      Y. Sugiyama
    • Journal Title

      Methods & Applications

      Volume: 73 Pages: 2230-2244

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Aronson-Benilan type estimate and the optimal Holder continuity of weak solutions for the1-D degenerate Keller-Segel systems2010

    • Author(s)
      Y. Sugiyama
    • Journal Title

      Revista Mathematica Iberoamericana

      Volume: 26 Pages: 891-913

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] ε-regularity theorem and its application to the blow-up solutions of Keller-Segel systems in higher dimensions2010

    • Author(s)
      Y. Sugiyama
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 364 Pages: 51-70

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic profile of blow-up solutions of Keller-Segel systems in super-critical cases2010

    • Author(s)
      Y. Sugiyama
    • Journal Title

      Differential Integral Equation

      Volume: 23 Pages: 601-618

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blow-up criterion via scaling invariant quantities with effect on coefficient growth in Keller-Segel system2010

    • Author(s)
      Y. Sugiyama
    • Journal Title

      Differential Integral Equation

      Volume: 23 Pages: 619-634

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-existence of backward self-similar solutions of the Keller-Segel system in the scaling invariant class2010

    • Author(s)
      H. Kozono and Y. Sugiyama, and R. Takada
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 365 Pages: 60-66

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Strong solutions to the Keller-Segel system with the weak L^<n/2> initial data and its application to the blow-up rate2010

    • Author(s)
      H. Kozono and Y. Sugiyama
    • Journal Title

      Math. Nachr.

      Volume: 283 Pages: 732-751

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness and regularity of weak solutions for the 1-$D$ degenerate Keller-Segel systems2010

    • Author(s)
      杉山由恵
    • Journal Title

      Nonlinear Analysis Series A : TMA

      Volume: 73 Pages: 2230-2244

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Aronson-B¥'{e}nilan type estimate and the optimal H¥"{o}lder continuity of weak solutions for the 1-$D$ degenerate Keller-Segel systems.2010

    • Author(s)
      杉山由恵
    • Journal Title

      Revista Mathematica Iberoamericana

      Volume: 26 Pages: 891-913

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic profile of blow-up solutions of Keller-Segel systems in super-critical cases2010

    • Author(s)
      杉山由恵
    • Journal Title

      Differential Integral Equations

      Volume: 23 Pages: 601-618

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-existence of backward self-similar solutions of the Keller-Segel system in the scaling invariant class2010

    • Author(s)
      小薗英雄, 杉山由恵, 高田了
    • Journal Title

      J.Math.Appl.Anal.

      Volume: 365 Pages: 60-66

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blow-up criterion via scaling invariant quantities with effect on coefficient growth in Keller-Segel system2010

    • Author(s)
      杉山由恵
    • Journal Title

      Differential Integral Equations

      Volume: 23 Pages: 619-634

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong solutions to the Keller-Segel system with the weak $L^{\frac{n}{2}}$ initial data and its application to the blow-up rate2010

    • Author(s)
      小薗英雄, 杉山由恵
    • Journal Title

      Math.Nachr

      Volume: 5 Pages: 732-751

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 走化性方程式-非線形拡散と移流項の相互作用について,日本応用数理学会学会誌「応用数理」特集:移流項をもつ反応拡散系2009

    • Author(s)
      杉山由恵
    • Journal Title

      日本応用数理学会

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Onε-regularity theorem and asymptotic behaviors of solutions for Keller-Segel systems2009

    • Author(s)
      Y. Sugiyama
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 41 Pages: 1664-1692

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Partial regularity and its application to the blow-up asymptotics of parabolic systems modelling chemotaxis with porous medium diffusion2009

    • Author(s)
      Y. Sugiyama
    • Journal Title

      Adv. Study in Pure Math.

      Volume: 55 Pages: 137-160

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Interfaces for1-D degenerate Keller-Segel systems2009

    • Author(s)
      Y. Sugiyama
    • Journal Title

      J. Evol.Equ.

      Volume: 9 Pages: 123-142

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in Lr(Rn)2009

    • Author(s)
      H. Kozono and Y. Sugiyama
    • Journal Title

      J. Differential Equations.

      Volume: 247 Pages: 1-32

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On $\epsilon$-regularity theorem and asymptotic behaviors of solutions for Keller-Segel systems2009

    • Author(s)
      Sugiyama, Yoshie
    • Journal Title

      SIAM J.Math.Anal. 41

      Pages: 1664-1692

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Partial regularity and its application to the blow-up asymptotics of parabolic systems modelling chemotaxis with porous medium diffusion2009

    • Author(s)
      Sugiyama, Yoshie
    • Journal Title

      Adv.Stud.Pure Math. 55

      Pages: 137-160

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces2009

    • Author(s)
      Kozono, Hideo, Sugiyama, Yoshie
    • Journal Title

      J.Differential Equations 247

      Pages: 1-32

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Interfaces for 1-D degenerate Keller-Segel systems2009

    • Author(s)
      Sugiyama, Yoshie
    • Journal Title

      J.Evol.Equ. 9

      Pages: 123-142

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Measure valued solutions of the 2D Keller-Segel system

    • Author(s)
      S. Luckhaus, Y. Sugiyama and J. J. L. Velazquez
    • Journal Title

      Archive for Rational Mechanics and Analysis

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Finite speed of propagation in 1-D degenerate Keller-Segel system

    • Author(s)
      Y. Sugiyama
    • Journal Title

      Math. Nachr

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness theorem of mild solutions to the Keller-Segel system in the scaling invariant space

    • Author(s)
      H. Kozono, Y. Sugiyama and T. Wachi
    • Journal Title

      J. Differential Equations

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Presentation] Asymptotic stability of stationary solutions to degenerate Keller-Segel systems2012

    • Author(s)
      Y.Sugiyama, Y.Yahagi
    • Organizer
      研究集会「拡散と移流の数理」
    • Place of Presentation
      九州工業大学(招待講演)
    • Year and Date
      2012-12-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] Asymptotic stability of stationary solutions to degenerate Keller-Segel systems2012

    • Author(s)
      Y.Sugiyama, Y.Yahagi
    • Organizer
      The 4^<th> TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis
    • Place of Presentation
      国立台湾大学(招待講演)
    • Year and Date
      2012-03-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] Asymptotic stability of stationary solutions to degenerate Keller-Segel systems2012

    • Author(s)
      Y.Sugiyama, Y.Yahagi
    • Organizer
      京都駅前セミナー
    • Place of Presentation
      龍谷大学(招待講演)
    • Year and Date
      2012-02-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] Asymptotic stability of stationary solutions to degenerate Keller-Segel systems2011

    • Author(s)
      Y.Sugiyama, Y.Yahagi
    • Organizer
      日本数学会関数方程式分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] Measure valued solutions of the 2D Keller-Segel system2011

    • Author(s)
      杉山由恵
    • Organizer
      第13回広島応用解析セミナー
    • Place of Presentation
      広島大学(招待講演)
    • Year and Date
      2011-08-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Asymptotic stability of stationary solutions to degenerate Keller-Segel systems「変分問題の展開-発展方程式論における変分的方法」2011

    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-06-06
    • Related Report
      2011 Final Research Report
  • [Presentation] Asymptotic stability of stationary solutions to degenerate Keller-Segel systems2011

    • Author(s)
      Y.Sugiyama, Y.Yahagi
    • Organizer
      京都大学数理解析研究所
    • Place of Presentation
      京都大学(招待講演)
    • Year and Date
      2011-06-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] Measure valued solutions of the 2D Keller-Segel system2011

    • Author(s)
      Y.Sugiyama
    • Organizer
      大阪市立大学談話会
    • Place of Presentation
      大阪市立大学(招待講演)
    • Year and Date
      2011-04-20
    • Related Report
      2011 Annual Research Report
  • [Presentation] Measure valued solutions of the 2D Keller-Segel system2011

    • Author(s)
      S.Luckhaus, Y.Sugiyama, J.J.L.Velazquez
    • Organizer
      京都大学NLPDEセミナー
    • Place of Presentation
      京都大学(招待講演)
    • Year and Date
      2011-04-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Measure valued solutions of the 2D Keller-Segel system2011

    • Author(s)
      杉山由恵
    • Organizer
      Seminario
    • Place of Presentation
      ICMAT(Spain)(招待講演)
    • Year and Date
      2011-02-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Measure valued solutions of the 2D Keller-Segel system2011

    • Author(s)
      杉山由恵
    • Organizer
      第16回早稲田大学「流体数学セミナー」
    • Place of Presentation
      早稲田大学(招待講演)
    • Year and Date
      2011-01-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Measure valued solutions of the 2D Keller-Segel, system2010

    • Author(s)
      杉山由恵
    • Organizer
      熊本における偏微分方程式研究集会
    • Place of Presentation
      熊本大学(招待講演)
    • Year and Date
      2010-11-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] Measure valued solutions of the2D Keller. Segel system「非線形の諸問題」2010

    • Place of Presentation
      山口大学
    • Year and Date
      2010-09-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Measure valued solutions of the 2D Keller-Segel system2010

    • Author(s)
      杉山由恵
    • Organizer
      第6回非線型の諸問題
    • Place of Presentation
      山口大学(招待講演)
    • Year and Date
      2010-09-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Measure valued solutions of the 2D Keller-Segel system2010

    • Author(s)
      杉山由恵
    • Organizer
      第48回解析ゼミ
    • Place of Presentation
      埼玉大学(招待講演)
    • Year and Date
      2010-06-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Extinction and decay for Keller-Segel systems of fast diffusion type2009

    • Organizer
      国際研究集会「Mathematical Analysis on the Navier-Stokes Equations and Related Topics, Past and Future
    • Place of Presentation
      神戸大学
    • Year and Date
      2009-12-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Extinction, decay and blow-up for Keller-Segel systems of fast diffusion type2009

    • Author(s)
      杉山由恵
    • Organizer
      日本数学会 関数方程式論分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2018-05-11  

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