2014 Fiscal Year Final Research Report
Research on profiles and the global bifurcation structure by explicit representation formula using elliptic functions
| Project/Area Number |
24540221
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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 | Ryukoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MORITA Yoshihisa 龍谷大学, 理工学部, 教授 (10192783)
MATSUMOTO Waichiro 龍谷大学, 理工学部, 教授 (40093314)
NINOMIYA Hirokazu 明治大学, 理工学部, 教授 (90251610)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 非線形境界値問題 / 完全楕円積分 / 楕円関数 / 交差拡散方程式 / 反応拡散方程式 / 極限方程式 / 弾性曲線 / 線形化固有値問題 |
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| Outline of Final Research Achievements |
We have deepened our original method and extended its range in order to solve various problems for differential equations. We obtain all the candidate solutions and derive transcendental equations equivalent to problems to be solved.
Especially, as for a cross-diffusion equation,we obtained the stability of stationary solutions in multidimensional case, which is inspired by 1 dimensional case results obtained by our method.
As for linearized eigen-value problems for reaction diffusion equations, we have obtained all exact values of eigen-values and representation formula of eigen-fuctions which have been thought impossible.
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| Free Research Field |
大域解析学
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