Keller-Segel systems of degenerate type

2008 Fiscal Year Final Research Report

• Project/Area Number: 18740080
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Tsuda College
• Principal Investigator: SUGIYAMA Yoshie Tsuda College, 学芸学部数学科, 准教授 (60308210)
• Project Period (FY): 2006 – 2008
• Keywords: 退化放物型 / ケーラ / ジーゲル系 / 解の爆発 / 発解の漸近挙動 / 有限伝播性 / 界面方程式

Research Abstract

科研費採択課題に関する上記研究期間中である平成18年度〜平成20年度に,10編の論文の掲載決定が決定された.更に10編の論文が現在投稿中である.
更に,以下の講演を行った.
講演(国内発表) 研究集会:2006年度15回・2007年度13回・2008年度5回(11月30日現在)
日本数学会:2006年9月〜2008年9月,計7講演(特別講演を含む)
講演(国際会議)
[1] 3rd Euro-Japanese workshop on blow up, 2008 9 11, Tohoku Univ.(招待講演)
[2] Hayashibara forum, 2006 11 23, フランス高等数学研究所(IHES).
[3] Parabolic and Navier-Stokes equations, 2006 9 11, Banach Center, Poland.
[4] 2nd Euro-Japanese workshop on blow up, 2006 9 7, Madrid, Spain.
[5] 第31回偏微分方程式論札幌シンポジウム, 2006 8 3, 北海道大学, 札幌.

Research Products

• [Journal Article] Partial regularity and its application to the blow-up asymptotics of parabolic systems modelling chemotaxis with porous medium diffusion (2009)
  • Journal Title: Adv.Study in Pure Math. 55 Pages: 137-160
• [Journal Article] Interfaces for 1-D degenerate Keller-Segel systems (2009)
  • Journal Title: J. Evol. Equ. 9 Pages: 123-142
• [Journal Article] Global solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in $L^r(R^n)$ (2009)
  • Journal Title: J. Differential Equations 247 Pages: 1-32
• [Journal Article] Local existence and finite time blow-up in the 2-D Keller-Segel system (2009)
  • Journal Title: J. Evol. Equ 8 Pages: 353-378
• [Journal Article] Keller-Segel system of parabolic-parabolic type with initial data in weak $L^{n/2}}(R^n)$ and its application to the self-similar solution (2009)
  • Journal Title: Indiana Univ. Math. J. 57 Pages: 1467-1500
• [Journal Article] Application of the best constant of the Sobolev inequality to degenerate Keller-Segel models (2007)
  • Journal Title: Adv.Differential Equations 12 Pages: 121-144
• [Journal Article] Asymptotic profile with the optimal convergence rate for a parabolic equation of chemotaxis in super-critical cases (2007)
  • Journal Title: Indiana Univ. Math. J. 56 Pages: 1279-1298
• [Journal Article] Time Global Existence and Asymptotic Behavior of Solutions to Degenerate Quasi-linear Parabolic Systems of Chemotaxis (2007)
  • Journal Title: Differential Integral Equations 20 Pages: 133-180
• [Journal Article] Global existence in the sub-critical cases and finite time blow-up in the super-critical cases to degenerate Keller-Segel systems (2006)
  • Journal Title: Differential Integral Equations 19 Pages: 841-876
• [Journal Article] Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems (2006)
  • Journal Title: Math. Model. Numer. Anal. 40 Pages: 597-621
• [Journal Article] Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term (2006)
  • Journal Title: J. Differential Equations 227 Pages: 333-364
• [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
  • Journal Title: RevistaMathematica Iberoamericana. to appear
• [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 rate
  • Journal Title: Math. Nachr. to appear
• [Presentation] Partial regularity and blow-up asymptotics of weak solutions to Keller-Segel systems (2009)
  • Organizer: Math. Biology : modelling and differential equations, Centre de Recerca Matematica
  • Place of Presentation: Autonoma Univ, Barcelona
  • Year and Date: 20090000
• [Presentation] Aronson-Benilan type estimate and the optimal Holder continuity of weak solutions for the 1D degenerate Keller-Segel systems (2009)
  • Organizer: 名古屋微分方程式研究集会
  • Year and Date: 20090000
• [Presentation] Aronson-Benilan type estimate and the optimal Hoelder continuity of weak solutions for the 1D degenerate Keller-Segel systems (2009)
  • Organizer: 金沢大学数理学談話会
  • Year and Date: 20090000
• [Presentation] Partial regularity and blow-up asymptoticsof weak solutions to Keller-Segel systems (2008)
  • Organizer: 3rd Euro-Japanese Workshop on Blowup
  • Place of Presentation: Tohoku Univ, invited speaker
  • Year and Date: 20080000
• [Presentation] Aronson-Benilan type estimate and the optimal Hoelder continuity of weak solutions for the 1D degenerate Keller-Segel systems (2008)
  • Place of Presentation: 東京大学
  • Year and Date: 20080000
• [Presentation] Aronson-B\'{e}nilan type estimate and the optimal H\"{o}lder continuity of weak solutions for the 1-D degenerate Keller-Segel systems (2008)
  • Place of Presentation: 東京理科大学
  • Year and Date: 20080000
• [Presentation] Interfaces for 1-D degenerate Keller-Segel systems (2008)
  • Organizer: 偏微分方程式セミナー
  • Place of Presentation: 中央大学
  • Year and Date: 20080000
• [Presentation] Finite speed of propagation in 1-D degenerate Keller-Segel system (2008)
  • Organizer: 広島微分方程式研究会
  • Place of Presentation: 広島大学
  • Year and Date: 20080000
• [Presentation] $\varepsilon$-regularity theorem and its application to the blow-up asymptotics of solutions to Keller-Segel systems (2008)
  • Place of Presentation: Complutense Univ, Madrid
  • Year and Date: 20080000
• [Presentation] $\varepsilon$-regularity theorem and its application to the blow-up solutions of degenerate Keller-Segel systems (2008)
  • Place of Presentation: 金沢大学
  • Year and Date: 20080000
• [Presentation] $\varepsilon$-regularity theorem and its application to the blow-up solutions of degenerate Keller-Segel systems (2008)
  • Organizer: 第24回九州における偏微分方程式研究集会
  • Year and Date: 20080000
• [Presentation] ε-regularity theorem and its application to blow-up asymptotics of weak solutions to degenerate Keller-Segel systems (2008)
  • Organizer: 語ろう数理解析
  • Year and Date: 20080000
• [Presentation] Interfaces for 1-D degenerate (2008)
  • Organizer: 日本数学会, 関数方程式論分科会
  • Year and Date: 20080000
• [Presentation] ε-regularity theorem and its application to the blow-up solutions of degenerate Keller-Segel systems (2008)
  • Organizer: 日本数学会, 関数方程式論分科会
  • Year and Date: 20080000
• [Presentation] $\varepsilon$-regularity theorem and its application to the blow-up solutions of degenerate Keller-Segel systems (2007)
  • Place of Presentation: 中央大学
  • Year and Date: 20070000
• [Presentation] $\varepsilon$-regularity theorem and its application to the blow-up solutions of degenerate Keller-Segel systems (2007)
  • Organizer: 神戸大学 解析セミナー
  • Place of Presentation: 神戸大学
  • Year and Date: 20070000
• [Presentation] $\varepsilon$-regularity theorem and its application to the blow-up solutions of degenerate Keller-Segel systems (2007)
  • Organizer: Nonlinear PDE seminar
  • Place of Presentation: 京都大学
  • Year and Date: 20070000
• [Presentation] Partial regularity and blow-up asymptotics of weak solutions to degenerate Keller-Segel systems (2007)
  • Organizer: Singularities arising in Nonlinear Problems 2007
  • Year and Date: 20070000
• [Presentation] 「複雑系現象の時系列解析」,「複雑系現象の時系列解析」 (2007)
  • Organizer: シンポジウム
  • Year and Date: 20070000
• [Presentation] Partial regularity and blow-up asymptotics of weak solutions to degenerate Keller-Segel systems (2007)
  • Organizer: COE transversal seminar on analysis and geometry
  • Year and Date: 20070000
• [Presentation] Gradient estimates and interfaces for degenerate Keller-Segel systems,「界面現象のダイナミクスを解明する最前線の数値解析とその展開III」 (2007)
  • Year and Date: 20070000
• [Presentation] Partial regularity of weak solutions to degenerate Keller-Segel systems (2007)
  • Organizer: 熊本大学応用解析セミナー
  • Year and Date: 20070000
• [Presentation] 走化性Keller-Segel 系の解の漸近挙動について (2007)
  • Organizer: 幾何学シンポジウム
  • Year and Date: 20070000
• [Presentation] Finite speed of propagation in degenerate 1-D Keller-Segel system (2007)
  • Organizer: 第四回非線形偏微分方程式研究集会
  • Place of Presentation: 加賀
  • Year and Date: 20070000
• [Presentation] Finite speed of propagation in degenerate Keller-Segel system (2007)
  • Organizer: 愛媛ワークショップ
  • Place of Presentation: 愛媛大学
  • Year and Date: 20070000
• [Presentation] On Keller-Segel System with a power factor in drift term (2007)
  • Organizer: 第6回偏微分方程式ワークショップ
  • Place of Presentation: 別府
  • Year and Date: 20070000
• [Presentation] On Quasi-linear Keller-Segel System (2007)
  • Organizer: 愛媛大学解析セミナー
  • Place of Presentation: 愛媛大学
  • Year and Date: 20070000
• [Presentation] 退化型Keller-Segel系の解の性質について (2007)
  • Organizer: 日本数学会, 関数方程式論分科会, 特別講演
  • Year and Date: 20070000
• [Presentation] Blow-up solutions to Keller-Segel systems for the initial data in the scale invariant norm (2007)
  • Organizer: 日本数学会, 関数方程式論分科会
  • Year and Date: 20070000
• [Presentation] Strong solutions to the Keller-Segel system with the weak Ln/2(Rn) initial data and its application to the blow-up rate (2007)
  • Organizer: 日本数学会, 関数方程式論分科会
  • Year and Date: 20070000
• [Presentation] Blow-up in Keller-Segel model (2006)
  • Organizer: Hayashibara forum
  • Place of Presentation: フランス高等数学研究所(IHES)
  • Year and Date: 20060000
• [Presentation] Asymptotic profile with optimal convergence rate for Keller-Segel model (2006)
  • Organizer: Parabolic and Navier-Stokes equations
  • Place of Presentation: Banach Center, Poland
  • Year and Date: 20060000
• [Presentation] Fujita exponent for Keller-Segel model (2006)
  • Organizer: 2nd Euro-Japanese workshop on blow up
  • Place of Presentation: Madrid, Spain.a
  • Year and Date: 20060000
• [Presentation] On the Keller Segel system in higher dimensions (2006)
  • Organizer: 第31回偏微分方程式論 札幌シンポジウム
  • Year and Date: 20060000
• [Presentation] Asymptotic profile for the degenerate Keller-Segel system (2006)
  • Organizer: 偏微分方程式セミナー
  • Place of Presentation: 横浜国立大学
  • Year and Date: 20060000
• [Presentation] On the Fujita exponent for Keller-Segel systems (2006)
  • Organizer: 福島応用数学小研究集会
  • Place of Presentation: 福島大学
  • Year and Date: 20060000
• [Presentation] On Fujita exponent for Keller-Segel system (2006)
  • Organizer: 偏微分方程式セミナー
  • Place of Presentation: 中央大学
  • Year and Date: 20060000
• [Presentation] Large time behavior of solutions to the degenerate Keller-Segel model (2006)
  • Organizer: 微分方程式セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 20060000
• [Presentation] On the Keller-Segel system in higher dimensions (2006)
  • Organizer: 第二回非線型の諸問題
  • Place of Presentation: 大分
  • Year and Date: 20060000
• [Presentation] On the Keller-Segel system and the Fujita exponent (2006)
  • Organizer: 解析セミナー
  • Place of Presentation: 慶応大学
  • Year and Date: 20060000
• [Presentation] On 3-D Keller-Segel system (2006)
  • Organizer: 談話会
  • Place of Presentation: 東京理科大学
  • Year and Date: 20060000
• [Presentation] Blow-up in Keller Segel system (2006)
  • Organizer: 北海道大学偏微分方程式セミナー
  • Year and Date: 20060000
• [Presentation] On the Fujita exponent for Keller-Segel systems (2006)
  • Organizer: 談話会
  • Place of Presentation: 東北大学
  • Year and Date: 20060000
• [Presentation] Asymptotic profile for solutions of Keller-Segel model 「微分方程式の粘性解理論とその発展」 (2006)
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 20060000
• [Presentation] Large time behavior of solutions in super-critical cases to Keller-Segel systems (2006)
  • Organizer: 函数方程式セミナー
  • Place of Presentation: 九州大学
  • Year and Date: 20060000
• [Presentation] Time-global solution and asymptotic behaviour for Keller-Segel models of semilinear and quasilinear degenerate type (2006)
  • Organizer: Conferencias de los Departamentos
  • Place of Presentation: Complutense Univ
  • Year and Date: 20060000
• [Presentation] Global solution and decay property for Keller-Segel system of semilinear and quasilinear type (2006)
  • Organizer: Zakladu Rownan Rozniczkowych IM UWr
  • Place of Presentation: Mathematical Institute of the Wroclaw University
  • Year and Date: 20060000
• [Presentation] Finite time blow-up for solution to Keller-Segel model of degenerate type (2006)
  • Place of Presentation: Autonoma Univ
  • Year and Date: 20060000
• [Presentation] Asymptotic profile for solutions of Keller-Segel model in super-critical cases (2006)
  • Organizer: 日本数学会, 関数方程式論分科会
  • Year and Date: 20060000
• [Presentation] Keller-Segel system of parabolic-parabolic type with initial data in weak Ln/2(Rn) and its application to the self-similar solution (2006)
  • Organizer: 日本数学会, 関数方程式論分科会
  • Year and Date: 20060000
• [Presentation] Asymptotic properties of reaction-diffusion systems modeling chemotaxis 2004 (2004)
  • Organizer: The Fourth World Congress of Nonlinear Analysts
  • Place of Presentation: Orlando, Florida, USA
  • Year and Date: 20040000
• [Presentation] Global existence of weak solutions and decay properties for some degenerate quasilinear parabolic systems modeling chemotaxis (2004)
  • Organizer: Workshop on Reaction-Diffusion Equations and Related Topics
  • Place of Presentation: National, Tsing Hua University, Hsinchu, Taiwan
  • Year and Date: 20040000