Mathematical models of elastic waves and their inverse problems
| Project/Area Number |
17540145
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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 | Ibaraki University |
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Principal Investigator |
SOGA Hideo IBARAKI University, the College of Education, Professor, 教育学部, 教授 (40125795)
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| Co-Investigator(Kenkyū-buntansha) |
KAIZU Satoshi IBARAKI University, the College of Education, Professor, 教育学部, 教授 (80017409)
NOZAKI Hideaki IBARAKI University, the College of Education, Professor, 教育学部, 教授 (60208337)
CHIBA Yasuo IBARAKI University, Center of University Education, Assistant Professor, 大学教育センター, 講師 (90400598)
NAKAMURA Gen HOKKAIDO University, the College of Science, Professor, 理学研究科, 教授 (50118535)
ITO Hiroya University of Electro-Communication, Department of Mathematics, Associate Professor, 電気通信学部, 助教授 (30211056)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | mathematical physics / inverse problems / elastic equations / seismic waves / scattering theory / Rayleigh wave / wave equations / partial differential equations / 偏微分方程 |
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| Research Abstract |
In this research project we aimed initially
(i) to examine scattering of surface waves (e.g. the Rayleigh wave, etc) and investigate inverse problems to extract the situations of the surface from the data of those waves ;
(ii) to set up some mathematical model corresponding the seismic probe and study inverse problems to know the shape of stratums from the data of reflected waves for artificial incident waves ;
(iii) to solve the above inverse problems numerically under typical conditions and make softwares of personal computers for exhibition of the propagation of the waves in the display.
About (i) : We have constructed a scattering theory of the Rayleigh wave and its asymptotic solution useful for solving the inverse problem, and a representation of the scattering kernel expressing the situations of the boundary. Furthermore, using these results, we have solved the inverse problem to get the information of the boundary from the date of the Rayleigh wave.
About (ii) : We have made an appropriate mathematical setup of the inverse problem of seismic waves and have developed the methods applied to it under some assumptions. But we have not been able to accomplish completely what we intended initially.
About (iii) : We have obtained a numerical algorism of optimal shape problems which seems applicable to the inverse problem. We have made a software of personal computers for exhibition of the propagation of the waves in the display. This will be developed to the one to show the situations of various setting of the inverse problem.
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Report
(3 results)
Research Products
(1 results)
