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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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 関数方程式 / 偏微分方程式 / 複素領域 / 特異点 / 形式解 / 正則性 / 合成積方程式 / 正則解 / 変換の方程式 |
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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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Report
(4 results)
Research Products
(43 results)
