Analysis of solutions to partial differential equations with piecewise smooth coefficients, and its application to inverse problems

现在我们考虑带有某些参数的偏微分方程。参数对偏微分方程的解有一定的影响。本研究的目的之一就是分析这些影响。在这段研究期间，我分析了带频率的偏微分方程逆问题的稳定性估计。特别地，我们处理了波动方程和薛定谔方程。因此，我得到了一些稳定性估计。这些稳定性估计告诉我们，当影响力变得更大时，稳定性变得更好。然而，不幸的是，现在我们不知道这个估计是否是最佳的。因此，我想继续分析这个问题。

Now we consider partial differential equations (PDEs) with some parameter. The parameter gives some influences for the solutions to PDEs. One of the aim of this research is to analyse such influences. In this study period, I analysed stability estimates for inverse problems of PDEs with frequency. In particular, we treated the wave equation and the Schroedinger equation. In consequence, I obtained some stability estimates. These stability estimates suggest us that stability becomes better when influence becomes large. However, unfortunately right now we do not know this estimate is optimal or not. Hence I would like to continue to analyse this problem.