2012 Fiscal Year Final Research Report
Development of Inverse problems via asymptotic analysis -from the point of view of scattering theory
| Project/Area Number |
22540194
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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 |
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| Co-Investigator(Renkei-kenkyūsha) |
IKEHATA Masaru 群馬大学, 大学院・工学研究科, 教授 (90202910)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 函数方程式 / 境界値逆問題 / 熱方程式 / 囲い込み法 / 散乱逆問題 |
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| Research Abstract |
The theme of this research is to analyze inverse boundary value problems for the heat equations by “enclosure method”. In the case that infinitely many measurements can be used, the expected results are obtained. In the case of one measurement, it is found that there are two different formulations. One is given by using similar thought to the case of infinitely many measurements. The other comes from a completely different idea. The latter one is much harder problem than former one. Even for the former problem, it is found that the distance between the boundary of the cavities or inclusions and the outside boundary is detected. Note that this amount is first caught in the setting of “enclosure method”. From the proofs of these results, it is clarified that “the length from the outside boundary to the point hitting inside boundary first” is detected.
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