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We survey some of our recent results on inverse problems for evolutionequations. The goal is to provide a unified approach to solve various types ofevolution equations. The inverse problems we consider consist in determiningunknown coefficients 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 andboundary lower order coefficients in wave and heat equations. Some of theresults presented here are slightly improved from their original versions.

A unified approach to solving some inverse problems for evolution equations by using observability inequalities