Mathematical analysis for the Lotka-Volterra system with nonlinear diffusion
| Project/Area Number |
24740101
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
KOUSUKE Kuto 電気通信大学, 情報理工学(系)研究科, 准教授 (40386602)
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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 |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 非線形拡散 / 数理生物学モデル / 楕円型方程式 / 分岐 / 極限系 / 移流 / 拡散の相互作用 / 反応拡散系 / 生物モデル / 楕円型偏微分方程式 / 非線形解析 / 偏微分方程式 / 現象の数理 / 分岐理論 / 縮約理論 / 安定性理論 |
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| Outline of Final Research Achievements |
This research studied the global structure of stationary solutions to the Lotka-Volterra system with nonlinear diffusion. Among other things, this research focused on the limiting system as the nonlinear diffusion term tends to infinity, which characterizes the limiting behavior of stationary solutions, and derived the curve of the set of non-constant solutions to the limiting system (the global bifurcation curve) in a functional space. As an example of results, this research proved that an element of unknown functions blows up as a bifurcation parameter approaches the second eigenvalue of the Laplace operator.
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Report
(4 results)
Research Products
(23 results)
