2011 Fiscal Year Final Research Report
Free boundary problems of PDEs with degeneracy-singularity and their applications
| Project/Area Number |
20740094
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Shibaura Institute of Technology (2011)
Kogakuin University (2008-2010) |
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Principal Investigator |
TAKEUCHI Shingo 芝浦工業大学, システム理工学部, 准教授 (00333021)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 非線形現象 / 解析学 / 微分方程式 / 自由境界 / 退化性 / 特異性 / p-Laplacian |
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| Research Abstract |
For a class of differential equations concerning change of the number of individuals, I discovered a singular mathematical construction and solved it by mathematically analyzing the nonlinearity. In particular, I defined a novel function which is a generalization of so-called Jacobian elliptic function and succeeded in describing the construction of the set of all solutions by representing all exact solutions in the form of the new function. In the future, I expect that studying the algebraic properties of the generalized Jacobian elliptic function, we can obtain new knowledge about differential equations, which could not be discovered in analytic approach.
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