2003 Fiscal Year Final Research Report Summary
Structure of solutions to the system of equations describing chemotactic aggregation of cellular slime molds
| Project/Area Number |
13640216
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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 |
Global analysis
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| Research Institution | HIROSHIMA UNIVERSIlY |
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Principal Investigator |
YOSHIDA Kiyoshi Hiroshima Univ., Faculty of Integrated Arts and Sciences, Prof., 総合科学部, 教授 (80033893)
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| Co-Investigator(Kenkyū-buntansha) |
USAMI Hiroyuki Hiroshima Univ., Faculty of Integrated Arts and Sciences, Ass. Prof., 総合科学部, 助教授 (90192509)
SHIBATA Tetsutaro Hiroshima Univ., Faculty of Integrated Arts and Sciences, Ass. Prof., 総合科学部, 助教授 (90216010)
NAGAI Toshitaka Hiroshima Univ., Graduate School of Science, Prof., 大学院・理学研究科, 教授 (40112172)
NAITO Yuki Kobe Univ., Faculty of Engineering, 工学部, 助教授 (10231458)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Keller-Segel system / Chirdress-Percus conjecture / global blanch / locations of blow up points / self-similar solution / elliptic equations / Lieuville type theorem / radially symmetrical solution |
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| Research Abstract |
Keller and Segel derived the mathematical model describing chemotactic aggregation of cellular slime molds which move toward high cocentrations of chemical substance. So this model is called as the Keller-Segel system. Chirdress and Percus conjectured that there exists a threshold number (8π) such that if an initial value is smaller than 8π, the solutions exist globally in time, on the other hand if an initial value is greater than 8π, the chemotactic collapse can occure. Our objective is to solve this conjecture. We study the Keller-Segel system in R^2 because this system is rarely studied in hole space. Especially we treated the self-similar solution and solved almost positively the Chirdress and Percus conjectuer. For this purpose we encountered several problems and solved these. We enumerate these problems : (1)determine decay order of the self-similar solutions (2)derive the Lieuville type theorem (3)reduction to one elliptic equation from an system of two elliptic equations (4)show the radial symmetry of solutions by using the moving plane method (5)determine the global blanch of solutions (6)solve the Chirdress and Percus conjectuer.
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