2012 Fiscal Year Final Research Report
Research on the asymptotic form of the solutions to the Helmholtz equation and the application to mathematical scattering theory
| Project/Area Number |
22540198
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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 |
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| Co-Investigator(Kenkyū-buntansha) |
NAKAZAWA Hideo 日本医科大学, 医学部, 教授 (80383371)
WATANABE Kazuo 学習院大学, 理学部, 助教 (90260851)
WATANABE Michiyuki 新潟大学, 人文社会教育科学系, 准教授 (90374181)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 半空間弾性波 / P 波と S 波 / レイリー波 / ヘルムホルツ方程式 / 定常位相の方法 |
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| Research Abstract |
We studied the solutions to the Helmholtz equation with respect to elastic wave in 3-dimensional half space with free boundary.Especially, we studied the asymptotic forms of infinite direction of space. As the results, we obtained the asymptotic forms concerning P mode, R mode, SV mode (the reflected P wave component only), SH mode and SV+SV0 mode (except for the reflected P wave component), respectively. But, for the asymptotic forms concerning SH mode and SV+SV0 mode, the direction of North pole was excepted. We also obtained the results concerning scattering and inverse scattering problem for wave equations with dissipative terms, inverse problem for nonlinear Schrodinger equations and the regularity (at interface) of the solutions to a system of first order partial differential equation as the related topics.
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