2002 Fiscal Year Final Research Report Summary
Research of the behavior of infinite time blowup solutions to systems related to chemotaxis and those blowup points
| Project/Area Number |
13640181
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Miyazaki University |
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Principal Investigator |
SENBA Takashi Miyazaki University, Faculty of Engineering, Professor, 工学部, 教授 (30196985)
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| 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)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Partial differential equation / Biology / Keller-Segel model / Blowup / Chemotaxis |
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| 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.
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