Study on inverse problems for partial differential equations using the probe and enclosure methods

本研究最具代表性的结果由两部分组成。第一个结果表明，利用有限时间范围内的动力学数据的封闭方法可以应用于若干三维热波方程和粘弹性方程组的反问题。研究结果也提出了几个有待解决的问题。第二个发现是将封闭法中的指示函数的对数微分应用于由亥姆霍兹方程控制的逆障碍物散射问题，其产生的信息是原始指示函数的两倍。

The most representative results obtained in this study consists of two parts. The first one shows that the enclosure method using dynamical data overa finite time interval can be applied to several inverse problems for the heat and waveequations and visco-elastic system of equations in three dimensions. And also the result raises several problems to be solved. The second one is the finding of the idea thatthe logarithmic differential of the indicator function in the enclosure method appliedto inverse obstacle scattering problems governed by the Helmholtz equation yieldsinformation two times more than the original indicator function.