2004 Fiscal Year Final Research Report Summary
Study of the singularities of solutions of partial differential equations
| Project/Area Number |
15540174
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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 | Ehime University |
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Principal Investigator |
IGARI Katsuju Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (90025487)
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| Co-Investigator(Kenkyū-buntansha) |
AMANO Kaname Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (80113512)
SADAMATSU Takasi Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (10025439)
ITO Hirosi Ehime University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (90243005)
MANDAI Takesi Osaka Electro-Communication University, Faculty of Engineering, Professor, 工学部, 教授 (10181843)
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| Project Period (FY) |
2003 – 2004
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| Keywords | singularities of solutions / analytic continuation / Fuchsian type / non-involutive double characteristics / Holmgren's uniqueness theorem / null solutions / asymptotic solutions |
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| Research Abstract |
1.Partial differential operators were considered in an n-dimensional complex domain, and, when the localization of the operator on its characteristic surface is Fuchsian type, it was proved that the singularities on the characteristic surface are removable. The result was applied to the propagation of singularities in the Cauchy problem for 2nd order equation with non-involutive double characteristics.
2.In a 2-dimensional space, the same kind of partial differential operators were studied and Holmgren's uniqueness theorem was extended to doubly characteristic points.
3.Partial differential operators with several Fuchsian variables were considered and the existence of distribution solution ( null solution) whose support is contained in a certain quadrant and contains the origin was proved.
4.The wellposedness of the Cauchy problem was studied for some degenerate parabolic equations and a necessary condition concerning the subprincipal symbol and the trace was given. It was proved by constructing asymptotic solutions.
5.As relevant studies, the numerical conformal mapping by using the charge simulation method were studied. The asymptotic behavior of scattering amplitude was also investigated for the Shrodinger operator with several point-like magnetic fields.
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