Project/Area Number  10640151 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Basic analysis

Research Institution  IBARAKI UNIVERSITY 
Principal Investigator 
SOGA Hideo IBARAKI Univ. Fac. of Education Prof., 教育学部, 教授 (40125795)

CoInvestigator(Kenkyūbuntansha) 
ITO Hiroya Univ. of ElectroComm. Dept Math. Assoc. Prof., 電通学部, 助教授 (30211056)
NAKAMURA Gen GUNMA Univ. Fac. of Technology Prof., 工学部, 教授 (50118535)
KAWASHITA Mishio IBARAKI Univ. Fac. of Education Assoc. Prof., 教育学部, 助教授 (80214633)
木村 真琴 茨城大学, 教育学部, 助教授 (30186332)
KAIZU Satoru IBARAKI Univ. Fac. of Education Prof., 教育学部, 教授 (80017409)
TANAKA Yasuo IBARAKI Univ. Fac. of Education Prof., 教育学部, 教授 (30007520)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 1999 : ¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1998 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  Elastic Waves / Wave Equations / Scattering Theory / Asymptotic Solutions / Reflection / Energy Decay / Mathematical Physics / Hyperbolic Equations / 弾性波 / 波動方程式 / 散乱理論 / 漸近解 / 反射 / エネルギー減衰 / 数理物理学 / 双曲型方程式 / 弾性方程式 / 表面波 / 全反射 / 逆問題 / 双曲系方程式 
Research Abstract 
This research project is concerned with elastic waves, and the main purposes set initially were a) to obtain concrete representations of the solutions, b) to study scattering of the waves near boundaries, c) to study inverse problems concerning the waves near boundaries, d) to analyze the waves in the case of the total reflection. We have accomplished these almost as was expected. Let us summarize the results obtained in this project. About a) and d) , we have got an asymptotic expansion of the wave reflected totally, which is one of the mainest results. This expansion is much expected to be useful in analyzing the phenomenon of the scattering and the inverse problems of the elastic waves. Furthermore, we have obtained also another kind of concrete representation of the waves. About b) , we have shown that the Rayleigh wave, which has been much interested since a long time ago, behaves individually and can be extracted in the LaxPhillips scattering theory : We have made a formulation of that theory for the Rayleigh wave, which is useful for the inverse problems. Moreover, we have investigated precisely decay of this wave expressing the behavior at infinity. About c) , we have got a new methods of reconstruction of coefficients in differential equations applicable to the inverse problems. And we have obtained a new numerical method of finite elements for the approximate solutions. These seem to be very useful to solve the inverse problems, but we cannot finish solving concretely some of the inverse problems.
