2003 Fiscal Year Final Research Report Summary
Scattering theory for the elastic surface waves
| Project/Area Number |
14540176
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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 | HIROSHIMA UNIVERSITY |
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Principal Investigator |
KAWASHITA Mishio Hiroshima University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (80214633)
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| Co-Investigator(Kenkyū-buntansha) |
SOGA Hideo Ibaraki University, Faculty of Education, Professor, 教育学部, 教授 (40125795)
IKEHATA Ryo Hiroshima University, Graduate School of Education, Associate Professor, 大学院・教育学研究科, 助教授 (10249758)
MORITA Takehiko Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00192782)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Surface waves / Scattering theory / Rayleigh waves / Lax-Phillips / Wilcox / wave equations |
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| Research Abstract |
The subject of the research is to clarify whether the surface waves propagating on boundaries of elastic medium can be regarded in the framework of the scattering theory or not. We obtain the following results on the problems about formulations of mathematical scattering theory suitable to analyzing the surface waves
(1) We can construct a formulation of the scattering theory of Lax and Phillips type
(2) We can find the diffences of scattering phenomena between the one for body waves and the one for surface waves
(3) For formulations of scattering theories with respect to hyprebolic problems, it was known that there were two differnt types (Wilcox type and Lax-Phillips type). We can show that those two types are equivalent each other using an abstract framework
From those results we can compair the scatteing theories obtained in the research and the previous ones
Our next concern is to clarify the properties of the scattered surface waves. For the purpose, we obtain the following results
(4) For surface waves propagating on the flat boundaries, How energies of them propagate
(5) A low frequency analysis of stationary waves on perturbed boundary
These results are expected to a basis on the further study of the properties of the surface waves
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