Research on estimation of the shape of unknown portions of a domain varying with time and on algorithms for reconstruction of the shape

当对象的面部的一部分的形状或对象的几个内腔的形状未知时，可以通过使用来自面部可访问部分的测量的热数据来估计形状。在本研究中，我们研究了形状随时间变化的这样一个反问题。然后重点研究了唯一判定问题：未知形状是否可以从热数据中唯一判定。反问题首先要求解决唯一判定问题。我们证明了唯一判定的一些充分条件。

When the shape of a portion of the face of an object or the shape of several internal cavities of an object is unknown, the shape may be estimated by using thermal data from measurements on an accessible portion of the face. In this research, we studied such an inverse problem for the shape which may vary with time. Then we focused on the unique determination problem: whether the unknown shape can be uniquely determined from the thermal data or not. Solving the unique determination problem is firstly requested for the inverse problem. We demonstrated some sufficient conditions for the unique determination.