| Project/Area Number |
61540077
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Ibaraki University |
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Principal Investigator |
SOGA Hideo Ibaraki University, 教育学部, 助教授 (40125795)
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| Co-Investigator(Kenkyū-buntansha) |
KUDO Kenji Ibaraki University, 教育学部, 助手 (00114017)
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| Project Period (FY) |
1986 – 1987
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| Project Status |
Completed (Fiscal Year 1987)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1987: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1986: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | Scattering theory / Inverse problems / Wave equations / Oscillatory integrals / Hyperbolic equations / Partial differential equations / The scattering kernel / Singular points / 散乱行列 |
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| Research Abstract |
In the latter half of 1986 and 1987 , we have studied the inverse problems of the scattering under several concrete assumptions.
At first, we have examined how the poles of the scattering matrix are distributed in the complex plane. M. Ikawa obtained a result concerning this examination. We have extended his result to more general case by means of the theorems derived by us in the previous year. This is discussed in <section>3 of the report of this grant, which is a copy of the paper published in Tsukuba J.Math. 11 (1987) 93-100.
Next, we have examined precisely the singular support of the scattering kernel in the case where the obstacle consists of two balls. Such problems are little studied although some foreign researchers begin to consider them recently. In cooperation with N. Nakamura (non-member of this grant), we have shown how closely the distribution of the points of this singular support is related with the distance of the two balls. This is described in <section>2 of the report of this grant. This section is a copy of the paper which will be published in J. Math. Soc. Japan 40 (1988).
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