| Project/Area Number |
11640174
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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 Takasi Miyazaki University, Faculty of Engineering, Assistant Professor, 工学部, 助教授 (30196985)
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| Co-Investigator(Kenkyū-buntansha) |
KAWANO Nichiro Miyazaki University, Faculty of Education and culture, Professor, 教育文化学部, 教授 (20040983)
KABEYA Yoshitsugu Miyazaki University, Faculty of Engineering, Assistant 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) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2000: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1999: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | Partial differential equation / Biology / Keller-Segel model / Blowup / Chemotaxis / Keller-Segel系 |
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| Research Abstract |
The aim of this research is as follows :
1. Research of radial blowup solutions to Keller-Segel model and a simplified Keller-Segel model referred to as Nagai model.
2. Research of stationary solutions to Keller-Segel model.
3. Research of the location of blowup points of solutions to Keller-Segel model and Nagai model.
Concerning with 1, Senba shows that the solution to Nagai model forms delta function singularities at the blowup time if the solution blows up in finite time. Moreover, Senba shows a similar result for solutions to Keller-Segel model, under the assumption of the isolation of blowup points. Those results are published in Adv. Differential Equations and Hiroshima Math.J..
Concerning with 2, regarding the L^1-norm of solutions as the parameter, Senba investigates areas of the parameter such that non-constant stationary solutions exist and do not exist, respectively. Kabeya shows the uniqueness of the radial and positive solution to some elliptic equations related to Keller-Segel model. We use Kabeya's result as the important information of the structure of stationary solutions to Keller-Segel model. The former and latter results are published in Adv.Math.Sci.Appl. and Comm.Partial.Differential Equations, respectively.
Concerning with 3, Senba shows that the blowup point of radial solutions to Keller-Segel model is the origin of the domain. Moreover, Senba shows that the location of blowup points of any blowup sequences of stationary solutions are controlled by Green function of a liner elliptic equation. However, we construct blowup solutions to Nagai model whose blowup points are independent of the Green function. That is to say, the result suggests that the location of blowup points of solutions to Keller-Segel model is not controlled only by the Green function. The first and second results are published in Hiroshima Math.J.and Adv.Math.Sci.Appl.. The third result will be published in Proceedings of the IMS Workshop on R.D.S..
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