1999 Fiscal Year Final Research Report Summary
Structure of the Solutions to Partial Differential Equations Degenerating on the Initial Surface
| Project/Area Number |
10640157
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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 (1999)
Gifu University (1998) |
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Principal Investigator |
MANDAI Takeshi Osaka Electro-Communication University, Faculty of Engineering, Professor, 工学部, 教授 (10181843)
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| Co-Investigator(Kenkyū-buntansha) |
IGARI Katsuju Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (90025487)
SHIGA Kiyoshi Gifu University, Faculty of Engineering, Professor, 工学部, 教授 (10022683)
TAHARA Hidetoshi Sophia University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (60101028)
SAKATA Sadahisa Osaka Electro-Communication University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60175362)
YAMAHARA Hideo Osaka Electro-Communication University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30103344)
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| Project Period (FY) |
1998 – 1999
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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 zero called characteristic exponent 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. Some conditions on the indicial polynomial have been assumed in most of the results. Mainly, we aimed to consider Fuchsian equations without any assumptions on the indicial polynomial. The main results are the following.
First, we could construct a solution map which gives the local structure the solutions to homogeneous single Fuchsian partial differential equations in a complex domain. We also had a similar result for Fuchsian systems of homogeneous equations.
We could also construct a solution to inhomogeneous Fuchsian equations, which is 'near' to a holomorphic solution.
Our idea seems to be applicable to wider range of problems, and we have already some results of extensions.
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