Free boundary problems of PDEs with degeneracy-singularity
Project/Area Number |
24540218
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Global analysis
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Research Institution | Shibaura Institute of Technology |
Principal Investigator |
TAKEUCHI Shingo 芝浦工業大学, システム理工学部, 教授 (00333021)
|
Project Period (FY) |
2012-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | p-Laplacian / 一般化ヤコビ楕円関数 / 一般化三角関数 / 完全楕円積分 / 算術幾何平均 / Legendreの関係式 / 超幾何関数 / ヤコビ楕円関数 / 楕円積分 / 退化特異 / 一般化楕円積分 / 基底 / 特殊関数 / 退化特異性 / 非線形拡散 |
Outline of Final Research Achievements |
Through this research project, the relation between the eigenfunctions of p-Laplacian and fundamental concepts of number theory, such as elliptic integral, elliptic function, hypergeometric function, arithmetic-geometric mean, etc., has come to be seen. We gave generalization of Jacobi elliptic function and the complete elliptic integral by generalized trigonometric functions, and as their application we presented Gauss-Legendre's type algorithm on the constant pi and generalization and expressions of solutions for classical differential equations. Regarding these series of results, we have received certain evaluations from P. Lindqvist, R. Manasevich, and M. Vuorinen, who are famous for research on p-Laplacian including generalized trigonometric functions, We believe that knowledge leading to cross-cutting research has been obtained.
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Report
(6 results)
Research Products
(41 results)
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[Presentation] 未定2016
Author(s)
竹内慎吾
Organizer
常微分方程式の定性的理論ワークショップ
Place of Presentation
島根大学
Year and Date
2016-09-22
Related Report
Invited
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