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Research of the behavior of infinite time blowup solutions to systems related to chemotaxis and those blowup points

Research Project

Project/Area Number 13640181
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionMiyazaki University

Principal Investigator

SENBA Takashi  Miyazaki University, Faculty of Engineering, Professor, 工学部, 教授 (30196985)

Co-Investigator(Kenkyū-buntansha) KABEYA Yoshitsugu  Miyazaki University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70252757)
TSUJIKAWA Tohru  Miyazaki University, Faculty of Engineering, Professor, 工学部, 教授 (10258288)
川野 日郎  宮崎大学, 教育文化学部, 教授 (20040983)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2001: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsPartial differential equation / Biology / Keller-Segel model / Blowup / Chemotaxis / 無限時刻爆発
Research Abstract

The aim of this research is the investigation of behavior of infinite time blowup solutions to Keller-Segel model and Nagi system which is a simplified system of Keller-Segel model. We get the following results.
(1) Behavior of infinite blowup solutions to Nagi system
Firstly, we show that quantities of some integrals of the solutions blow up in infinite time, the blowup point is only the origin of the domain, and that the concentrating mass at the blowup point is equal to the threshold number determining the coefficient of Nagi system. The result is published in Nonlinear Analysis. Secondly, we show the above result without the assumption of radical symmetric. Here, we show that the concentrating mass is equal to threshold number in the case where the blowup point is in the domain, and that the concentrating mass is equal to the half of the threshold number in the case where the blowup point is on the boundary. In order to show the result, we show a compactness of solutions and develop the method of the spatial localized rearrangement. The result is published in Asymptotic Analysis.
(2) Behavior of finite time blowup solutions to Jager-Luchkhaus system
Applying the compactness of solutions and the method of the spatial localized rearrangement mentioned above to radial symmetric solutions of Jager-Luchkhaus system, which is another simplified system of Keller-Segel model, we show that the concentrating mass at the blowup point is equal to threshold number for finite time blowup solution whose rescaled solutions blow up at infinite time. We presented the result in the international conference and the Mathematical Society of Japan.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (28 results)

All Other

All Publications (28 results)

  • [Publications] Takasi Senba: "Time global solutions to a parabolic-elliptic system modelling chemotaxis"Asymptotic Analysis. 32. 63-89 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takasi Senba: "Behavior of solutions to a system related to chemotaxis"Nonlinear Analysis. 47. 2551-2562 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takasi Senba: "Parabolic system of chemotaxis : Blowup in a finite and the infinite time"Methods and Applications of Analysis. 8・2. 349-368 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Koichi Osaki: "Exponential attractor for a chemotaxis-growth system of equations"Nonlinear Analysis. 51. 119-144 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Tohru Tsujikawa: "Exponential attractor for an adsorbate-induced phase transitions model"Kyushu Journal of Mathematics. 56・2. 313-336 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yoshitsugu Kabeya: "Behavior of least-energy solutions to Matukuma type equations"Journal of the Mathematical Society of Japan. 54・4. 937-973 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yoshitsugu Kabeya: "Blowup rate of solutions to the Brezis-Nireberg equations with the Robin condition"Funkcialaj Ekvacioj. 45・2. 291-318 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yoshitsugu Kabeya: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Communications on Pure and Applied Analysis. 1・1. 85-102 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takashi Senba and Takashi Suzuki: "Time global solutions to a parabolic-elliptic system modeling chemotaxis"Asymptotic Analysis. 32. 63-89 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takashi Senba and Takashi Suzuki: "Behavior of solutions to a system related to chemotaxis"Nonlinear Analysis. 47. 2551-2562 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takashi Senba and Takashi Suzuki: "Parabolic system of chemotaxis: Blowup in a finite and the infinite time"Methods and Applications of Analysis. 8-2. 349-368 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Koichi Osaki, Tohru Tsujikawa, Atsushi Yagi and Masayasu Mimura: "Exponential attractor for a chemotaxis-growth system of equations"Nonlinear Analysis. 51. 119-144 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Tohru Tsujikawa and Atsushi Yagi: "Exponential attractor for an absorbate-induced phase transition model"Kyushu Journal of Mathematics. 56-2. 313-336 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yoshitsugu Kabeya: "Behavior of least-energy solutions to Matukuma type equations"Journal of the Mathmatical Society of Japan. 54-4. 937-973 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yoshitsugu Kabeya: "Blowup rate of solutions to the Brezis-Nirenberg equations with the Robin condition"Funkcialaj Ekvacioj. 45-2. 291-318 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Yoshitsugu Kanbe, Eiji Yanagida and Shoji Yotsutani: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Communications on Pure and Applied Analysis. 1-1. 85-102 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takasi Senba: "Time global solutions to a parabolic-elliptic system modelling chemotaxis"Asymptotic Analysis. 32. 63-89 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Takasi Senba: "Behavior of solutions to a system related to chemotaxis"Nonlinear Analysis. 47. 2551-2562 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Takasi Senba: "Parabolic system of chemotaxis : Blowup in a finite and the infinite time"Methods and Applications of Analysis. 8・2. 349-368 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Koichi Osaki: "Exponential attractor for a chemotaxis-growth system of equations"Nonlinear Analysis. 51. 119-144 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tohru Tsujikawa: "Exponential attractor for an adsorbate-induced phase transitions model"Kyushu Journal of Mathematics. 56・2. 313-336 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Yoshitsugu Kabeya: "Behavior of least-energy solutions to Matukuma type equations"Journal of the Mathematical Society of Japan. 54・4. 937-973 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Yoshitsugu Kabeya: "Blowup rate of solutions to the Brezis-Nirenberg equations with the Robin condition"Funkcialaj Ekvacioj. 45・2. 291-318 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Yoshitsugu Kabeya: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Communications on Pure and Applied Analysis. 1・1. 85-102 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Takasi Senba: "Behavior of solutions to a system related to chemotaxis"Nonlinear Anal.. 47. 2551-2561 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Toshitaka Nagai: "Concentration behavior of blow-up solutions for a simplified system of chemotaxis"数理解析研究所 講究録. 1181. 140-177 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Takasi Senba: "Parabolic system of chemotaxis : Blowup in a finite and the infinite time"Meth. Appl. Anal.. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Yoshitsugu Kabeya: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Comm. Pure Appl. Anal.. 1・1. 85-102 (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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