2002 Fiscal Year Final Research Report Summary
Study on differential equations by asymptotic analysis
| Project/Area Number |
13640191
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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 |
UCHIYAMA Koichi Sophia Univ. Math. Professor, 理工学部, 教授 (20053689)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHINO Kunio Sophia Univ. Math. Lecturer, 理工学部, 講師 (60138378)
TAHARA Hidetoshi Sophia Univ. Math. Professor, 理工学部, 教授 (60101028)
OUCHI Sunao Sophia Univ. Math. Professor, 理工学部, 教授 (00087082)
HIRATA Hitoshi Sophia Univ. Math. assistant, 理工学部, 助手 (20266076)
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| Project Period (FY) |
2001 – 2002
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| Keywords | asymptotic analysis / differential equation / singularity / complex domain / integral representation / multi summability / Briot-Bouquet / Maillet |
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| Research Abstract |
A. Asymptotic analysis of differential equations in the complex domain.
S.Ouchi obtained integral representations of solutions with singularities of power type for a class containing Fuchsian linear PDEs and gave asymptotic behavior of solutions and Gevrey type estimates. He also proved multisummability of formal solutions to a class of linear PDEs he conjectured. H.Tahara, with H. Chen and Z.Luo, proved theorems of Maillet type for formal solutions to nonlinear PDEs with irregular singularity respect to space variables. He also obtained with J. Lope a sharp result on analytic continuation of solutions to a class of nonlinear PDEs of normal type. With H.Yamazawa, he determined the structure of solutions to a class of nonlinear PDEs of Fuchsian type without additional conditions on characteristic exponents.
B. Asymptotic analysis of differential equations in the real domain and related applied analysis.
K.Uchiyama, with L.Paredes, gave analytic expressions of solutions near their singularities for a nonlinear ODE, one dimensional p-elliptic Eq, using nonlinear ODE of Briot-Bouquet type in the complex domain. K.Yoshino characterized tempered distributions with support contained in convex proper cone, by asymptotic behavior of solutions to the heat equation, after T. Matsuzawa. H.Hirata gave relation between nonlinear parameter and the initial value space of semilinear Pintegro-DifiE interpolating the heat equation and the wave equation. He also constructed concrete solutions by Backlund transformations applied to trivial solutions to a certain 3rd order nonlinear PDE. S.Goto studied subfactors in operator algebra to compute principal graphs and to classify subfactors. M.Aoyagi studied numerical algorithms concerning triangle recognition, necessary for recognition of obstacles as complex after division of tetraheds after division of 3-dim obstacles.
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