Study on reaction-diffusion equations and related free boundary problems
| Project/Area Number |
24540220
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Waseda University |
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Principal Investigator |
YAMADA Yoshio 早稲田大学, 理工学術院, 教授 (20111825)
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| Co-Investigator(Renkei-kenkyūsha) |
OTANI Mitsuharu 早稲田大学, 理工学術院, 教授 (30119656)
TANAKA Kazunaga 早稲田大学, 理工学術院, 教授 (20188288)
HIROSE Munemitsu 明治大学, 理工学部, 准教授 (50287984)
NAKASHIMA Kimie 東京海洋大学, 海洋科学部, 准教授 (10318800)
TAKEUCHI Shingo 芝浦工業大学, システム理工学部, 准教授 (00333021)
KUTO Kousuke 電気通信大学, 情報理工学研究科, 准教授 (40386602)
WAKASA Tohru 九州工業大学, 工学研究院, 准教授 (20454069)
OEDA Kazuhiro 早稲田大学, グローバルエデュケーションセンター, 助教 (70580364)
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| Research Collaborator |
KANEKO Yuki
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 反応拡散方程式 / 自由境界問題 / 数理生態学 / 非線形現象 / 正値定常解 / 非局所項 / ロジスティック方程式 / 漸近挙動 / 大域的漸近安定性 / 非局所問題 |
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| Outline of Final Research Achievements |
This research is concerned with a free boundary problem for reaction-diffusion equations in mathematical ecology. This problem models the invasion or migration of a certain biological species. Our main interest is to study the evolution of the population density and habitat of the species. The population density is described by a reaction-diffusion equation and the boundary (or a part of the boundary) of the habitat is controlled by a free boundary condition of Stefan type. We could obtain theoretical understanding on asymptotic behaviors of solutions for free boundary problems of various types: whether the species vanishes eventually or the species persists with spreading free boundary. Moreover, we got precise results on the spreading speed of the free boundary.
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Report
(4 results)
Research Products
(28 results)
