2002 Fiscal Year Final Research Report Summary
Structure of the Solutions to Partial Differential Equations Degenerating on the Initial Surface, and its Applications
| Project/Area Number |
12640194
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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 | Osaka Electro-Communication University |
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Principal Investigator |
MANDAI Takeshi Faculty of Engineering, Professor, 工学部, 教授 (10181843)
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| Co-Investigator(Kenkyū-buntansha) |
ASAKURA Fumioki Faculty of Engineering, Professor, 工学部, 教授 (20140238)
TAHARA Hidetoshi Sophia University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (60101028)
IGARI Katsuju Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (90025487)
YAMAHARA Hideo Faculty of Engineering, Associate Professor, 工学部, 助教授 (30103344)
SAKATA Sadahisa Faculty of Engineering, Associate Professor, 工学部, 助教授 (60175362)
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| Project Period (FY) |
2000 – 2002
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| Keywords | Fuchsian partial differential equations / regular singularity / method of Frobenius / characteristic exponent / characteristic Cauchy problem |
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| Research Abstract |
The indicial polynomial and its zeros called characteristic exponents play an important role in the study of Fuchsian partial differential equations in the sense of Baouendi-Goulaouic, that is, linear partial differential equations with regular singularity along the initial surface. We had succeeded to construct a solution map which gives the local structure of the solutions to homogeneous single Fuchsian partial differential equations and first order Fuchsian systems in a complex domain, without any assumption on the indicial polynomial.
In this research, we constructed a solution map for Fuchsian systems of Volevic type (not necessarily first order). We need to consider the systems without reducing them to first order systems, since such a reduction involves singular transformations.
We also considered partial differential equations with several Fuchsian variables. We constructed distribution null-solutions for such equations in the real domain. The situation is far more complicated than that for equations with a single Fuchsian variable, for which we had already constructed distribution null-solutions.
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