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

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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.