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Structure of solutions to Keller-Segel system

Research Project

Project/Area Number 11640203
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionHIROSHIMA UNIVERSITY

Principal Investigator

YOSHIDA Kiyoshi  Hiroshima Univ., Integrated Arts and Sciences, Prof., 総合科学部, 教授 (80033893)

Co-Investigator(Kenkyū-buntansha) TANAKA Kazunaga  Waseda Univ., Science and Engineering, Prof., 理工学部, 教授 (20188288)
MIZUTA Yoshihiro  Hiroshima Univ., Integrated Arts and Sciences, Prof., 総合科学部, 教授 (00093815)
NAGAI Toshitaka  Hiroshima Univ., Graduate Scholl of Science, Prof., 大学院・理学研究科, 教授 (40112172)
NAITO Yuki  Kobe Univ., Engineering, Ass.Prof., 工学部, 助教授 (10231458)
USAMI Hiroyuki  Hiroshima Univ., Integrated Arts and Sciences, Ass.Prof., 総合科学部, 助教授 (90192509)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2000: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1999: ¥1,600,000 (Direct Cost: ¥1,600,000)
KeywordsKeller-Segel system / Self-similar solution / global blanch / locations of blow up points / chemotactic collapse / elliptic equation / oscllation problem / Sobolev functions / 楕円型方程式 / 爆発 / 大域解 / 固有値問題 / 双曲型方程式
Research Abstract

T.Nagi, Y.Naito and K.Yoshida studied the Keller-Segel system which is the mathematical model describing chemotactic aggregation of cellular slime molds which move toward high cocentrations of chemical substance. Naito and Yoshida with N.Muramoto studied the self-similar solution to the Keller-Segel system. Then the Keller-Segel system is reduced to an elliptic equation with an parameter σ, and obtained solutions of two types, one of which is in a low critical lebel, the other is in a high cirtical lebel. When the parameter is large, there is no self-similar radial solution. This means two solutions are connected by a global blanch. Nagai with T.Senba and T.Suzuki considered the location of blow-up points. These results are announced at each conference or workshop e.g, IMS Workshop on Reaction-Diffusion Systems at HongKong (December 6-10, 1999), The Third World Congress of Nonlinear Analysis at Catania (July 19-26, 2000). H.Usami treated the oscillation problem to the second order ordinary differential equations and the asymptotic properties of the variational eigenvalues. Y.Mizuta completed the results by Koskela concerning the uniqueness property for Sobolev functions.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (29 results)

All Other

All Publications (29 results)

  • [Publications] T.Nagai: "Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains,"Journal of Inequalities and Applications. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Nagai,T.Suzuki and T.Senba: "Chemotactic collapse in a parabolic system of mathematical biology"Hiroshima Math.J.. 30. 463-497 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Mizuta and T.Shimomura: "Boundary limits of spherical means for BLD abd monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 26. 45-60 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Mizuta and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 24・2. 457-465 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Naito and H.Usami: "Oscillation criteria for quasilinear elliptic equations"Nonlinear Analysis. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.Muramoto,Y.Naito and K.Yoshida: "Existence of self-similar solutions to a parabolic system modelling chemotaxis"Japan J.Indust.Appl.Math.. 17・3. 427-451 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Mizutani,N.Muramoto,K.Yoshida: "Self-similar radial soluitons to a parabolic system modelling chemotaxis via variational method"Hiroshima Math.J.. 29. 145-160 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] N.Muramoto, Y.Naito and K.Yoshida: "Existence of self-similar solutions to a parabolic system modelling chemotaxis"Japan J.Indust.Appl.Math.. 17. 427-451 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Mizutani, N.Muramoto and K.Yoshida: "Self-similar radial soluitons to a parabolic system modelling chemotaxis via variational method"Hiroshima Math.J.. 29. 145-160 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Nagai: "Behavior of solutions to a parabolic-elliptic system modelling chemotaxis"J.Korean Math.Soc.. 37. 721-733 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Nagai, T.Senba and T.Suzuki: "Chemotactic collapse in a parabolic system of mathematical biology"Hiroshima Math.J.. 30. 463-497 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Mizuta and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Ann.Acad.Sci.Fenn.Math.. 25. 457-465 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Mizuta and T.Shimomura: "Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball"Ann.Acad.Sci.Fenn.Math.. 24. 45-60 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Naito and H.Usami: "Oscillation criteria for quasilinear elliptic equations"Nonlinear Analysis T.M.A.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Kamo and H.Usami: "Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations"Adv.Math.Sci.Appl.. 10. 673-688 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Nagai: "Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains,"Journal of Inequalities and Applications. (発表予定).

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Nagai,T.Suzuki and T.Senba: "Chemotactic collapse in a parabolic system of mathematical biology"Hiroshima Math.J.. 30. 463-497 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Mizuta and T.Shimomura: "Boundary limits of spherical means for BLD abd monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 26. 45-60 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Mizuta and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 24・2. 457-465 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Naito and H.Usami: "Oscillation criteria for quasilinear elliptic equations"Nonlinear Analysis. (発表予定).

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Muramoto,Y.Naito and K.Yoshida: "Existence of self-similar solutions to a parabolic system modelling chemotaxis"Japan J.Indust.Appl.Math.. 17・3. 427-451 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y.Mizutani,N.Muramoto,K.Yoshida: "Self-similar radial soluitons to a parabolic system modelling chemotaxis via variational method"Hiroshima Math.J.. 29. 145-160 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Nagai: "Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains,"Journal of Inequalities and Applications. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Nagai,T.Suzukiand T.Senba: "Chemotactic collapse in a parabolic system of mathematical biology"Hiroshima Math.J.. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Mizuta and T.Shimomura: "Boundary limits of spherical means for BLD abd monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I..Math.. 26. 45-60 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Mizuta and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I..Math.. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Mizuta: "Multiple exponential integrability for Riesz potentials of functions in Orlicz classes"Advances in Math.Sci. and Applications. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Mizutani,N.Muramoto,K.Yoshida: "Self-similar radial solutions to a parabolic modelling chemotaxis via variational method"Hiroshima Math.J.. 29. 145-160 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] N.Muramoto,Y.Naito and K.Yoshida: "Existance of self-similar solutions to a parabolic system modelling chemotaxis"Japan J.Indust.Appl.Math.. (発表予定).

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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