2009 Fiscal Year Final Research Report
A STUDY OF SINGULARITIES IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS IN THE COMPLEX DOMAIN
| Project/Area Number |
19540197
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Sophia University |
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Principal Investigator |
TAHARA Hidetoshi Sophia University, 理工学部, 教授 (60101028)
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| Co-Investigator(Kenkyū-buntansha) |
OUCHI Sunao 上智大学, 理工学部, 教授 (00087082)
UCHIYAMA Koichi 上智大学, 理工学部, 名誉教授 (20053689)
KATO Masahide 上智大学, 理工学部, 教授 (90062679)
HIRATA Hitoshi 上智大学, 理工学部, 講師 (20266076)
YOSHINO Kunio 東京都市大学, 知識工学部, 教授 (60138378)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 関数方程式 / 偏微分方程式 |
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| Research Abstract |
We studied singularities of solutions of nonlinear partial differential equations in the complex domain, and obtained the following results. (1) In the case of Briot-Bouquet type partial differential equations, we determined all solutions which have singularities on a hypersurface. (2) We proved a sharp form of the uniqueness of the solution of nonlinear totally characteristic type partial differential equations, which yields the non-existence of singularities. (3) We constructed solutions with logarithmic singularities to certain nonlinear partial differential equations. (4) We determined asymptotic expansions of solutions of nonlinear partial differential equations of non-Kowalewskian type by using Mellin transformations.
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Research Products
(22 results)
