| Project/Area Number |
09640204
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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 |
解析学
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| Research Institution | KYUSHU INSTITUTE OF TECHNOLOGY |
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Principal Investigator |
NAGAI Toshitaka KYUSHU INSTITUTE OF TECHNOLOGY,Faculty of Engineering, Professor, 工学部, 教授 (40112172)
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| Co-Investigator(Kenkyū-buntansha) |
SENBA Takashi Miyazaki University, Faculty of Technology, Associate Professor, 工学部, 助教授 (30196985)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | Advection-diffusion system / Global existence of solutions / Blow-up of solutions / Singularity of solutions / 移流拡散方程式 / 解の時間大域的存在 / 解の挙動 / 関数の対称化 |
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| Research Abstract |
The purpose of this research is to study the qualitative properties of an advection-diffusion equationcalled a chemotaxis system. This system is a mathematical model describing chemotactic aggregation of cellular slime molds which move towards relatively higher concentration of a chemical. We studied the global existence of solutions and finite-time blow-up of solutions to the chemotaxis system and obtained the following results.
1. Two types of sensitivity functions are considered to study the structure of the global existence and blow-up of solutions, and it was shown that the structure of radial solutions entirely depends on the sensitivity functions.
2. It was shown that the finite-time blow-up of solutions to an parabolic-elliptic system, which is a simplified version of the chemotaxis system, necessarily leads to chemotactic collapse (the blow-up with 6-function singularities) at an isolated blow-up point in two-dimensional domains.
3. The application of syrnmetrization techniques to the parabolic-elliptic system mentioned above is effective to obtain Dr-estimates of solutions in terms of L^p norm of initial functions.
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