Development of Inverse problems via asymptotic analysis -from the point of view of scattering theory

点击翻译按钮获取中文摘要

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.