2014 Fiscal Year Final Research Report
A STUDY OF SINGULARITIES OF SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS IN THE COMPLEX DOMAIN
| Project/Area Number |
22540206
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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 |
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Keywords | 偏微分方程式 / 複素領域 / 正則解 / 特異点 / 形式解 / ボレル総和法 |
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| Outline of Final Research Achievements |
We studied solutions and their singularities of nonlinear partial differential equations in the complex domain, and obtained the following results. (1) We proved the existence and the uniqueness of the solution of nonlinear partial differential equations of various types. (2) In the case of Briot-Bouquet type partial differential equations with a positive integral characteristic exponent, we determined all solutions which have singularities on a hypersurface. (3) We proved the multisummability of formal solutions to linear partial differential equastions of non-Kowalevskian type. (4) We studied q-analogues of Laplace and Borel transforms, and applied it to linear q-difference partial differential equations.
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| Free Research Field |
偏微分方程式論
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