| Project/Area Number |
25400180
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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 |
Mathematical analysis
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
JIMBO Shuichi 北海道大学, 大学院理学研究院, 教授 (80201565)
TANAKA Kazunaga 早稲田大学, 大学院理工学術院, 教授 (20188288)
SHIBATA Tetsutaro 広島大学, 大学院工学研究科, 教授 (90216010)
SHIBATA Masataka 東京工業大学, 大学院理工学研究科, 助教 (90359688)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 変分問題 / 最適化問題 / 固有値問題 / 非線形楕円型偏微分方程式 / パターン形成 / 非線形楕円型方程式 / ボーズ・アインシュタイン凝縮 / パターン形成問題 / 数理生態学 / 数学解析 / 固有値漸近挙動 |
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| Outline of Final Research Achievements |
In this research, we studied the structure of solutions of nonlinear elliptic
partial differential equations arising in mathematical models of quantum phenomena and pattern formation problems of the mathematical biology. Especially, we investigated the precise asymptotic behavior of eigenvalues of the Laplacian with the mixed boundary condition on a thin domain and the precise asymptotic behavior of the least energy of a nonlinear variational problem associated with the Bose-Einstein condensation. We also studied the structure of global minimizers for 3-component FitzHugh-Nagumo system and the parameter range of existence and non-existence of non-constant steady patterns for several nonlinear rection-diffusion systems, e.g., the prey-predator model with a cross-diffusion effect.
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