A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities (CSIAM Transactions on Applied Mathematics, 2020)
We survey some of our recent results on inverse problems for evolutionequations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknowncoefficients from boundary measurements by varying initial conditions. Based on observability inequalities and a special choice of initial conditions, we provide uniqueness and stability estimates for the recovery of volume and boundary lower order coefficients in wave and heat equations. Some of the results presented here are slightlyimproved from their original versions.
Keywords: Evolution equations; Laplace-Beltrami operator; observability inequality; geometric control; initial-to-boundary operator.