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

本研究的主题是用“封闭法”分析热方程的反边值问题。在可以使用无限次测量的情况下，可以得到预期的结果。在一次测量的情况下，发现有两种不同的公式。一个是用与无限次测量类似的思想得到的。另一个则来自一个完全不同的想法。后一个问题比前一个困难得多。即使对于前一个问题，也可以检测到腔或夹杂物的边界与外部边界之间的距离。请注意，此金额首先捕获在“封装方法”的设置。通过对这些结果的证明，明确了检测“从外边界到先击中内边界的点的长度”。

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.