2015 Fiscal Year Final Research Report
The asymptotic behavior of Green function for wave propagation with some singularities and the applications to scattering theory
| Project/Area Number |
25400173
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | The University of Shiga Prefecture (2015)
Ehime University (2013-2014) |
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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) |
2013-04-01 – 2016-03-31
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| Keywords | 音響波動伝播 / 弾性波動伝播 / レゾルベント / 散乱振幅 / 一般化されたフーリエ変換 / 摩擦項を伴う波動方程式 / マクセル方程式 / 解の正則性 |
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| Outline of Final Research Achievements |
We studied the asymptotic behavior of Green functions concerning wave propagation having refraction phenomena. Moreover, as the applications, we studied scattering theory of such wave propagation. Especially, we analyzed Green functions concerning wave propagation in two layered media of three dimensional space. And using this result, we proved that scattering wave consists of two kinds of spherical wave characterized by each medium. Here, scattering wave means reflective wave which is occurred by a plane wave being incident on an obstacle. Moreover, by same method as in this research, we obtained similar results concerning three dimensional elastic wave propagation in a half space with free boundary condition. As related results, we also obtained results concerning estimations for solutions to stationary wave equations with dissipative terms and the regularity at interface of the solutions to Maxwell equations, respectively.
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| Free Research Field |
数学的散乱理論
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