2003 Fiscal Year Final Research Report Summary
Study of singularities of solutions of partial differential equations in the complex domain
| Project/Area Number |
14540185
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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, Faculty of Science and Technology, Professor, 理工学部, 教授 (60101028)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHINO Kunio Sophia University, Faculty of Science and Technology, Lecturer, 理工学部, 講師 (60138378)
UCHIYAMA Koichi Sophia University, Faculty of Science and Technology, Professor, 理工学部, 教授 (20053689)
OUCHI Sunao Sophia University, Faculty of Science and Technology, Professor, 理工学部, 教授 (00087082)
YAMANE Hideshi Kansei Gakuin University, Faculty of Science and Technology, Ass.Professor, 理工学部, 助教授 (80286145)
OKADA Yasunori Chiba University, Faculty of Science, Ass.Professor, 理学部, 助教授 (60224028)
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| Project Period (FY) |
2002 – 2003
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| Keywords | complex domain / PDE / holomorphic solution / singularity / analytic continuation |
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| Research Abstract |
1.Singularities of solutions of partial differential equations in the complex domain were studied and the followingresults were obtained:
(1)Structure of singular solutions of nonlinear Fuchsian type partial differential equations were determined completely without any assumptions on characteristic exponents.
(2)A sharp result was obtained on the existence and non-existence of singular solutions of non-linear first order partial differential equations of normal type.
2.A formal power series solutions of partial differential equations and its analytic meanings were studied and the following result was obtained: every formal power series solutions of certain class of linear partial differential equations are multisummable.
3.Analytic singularities of solutions of non-linear partial differential equations concerning p-elliptic equation were studied. By using a result on Fuchsian partial differential equations, it was proved that every fractional type singularity of solutions is an analytic singularity.
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