(REVIEW ARTICLE) A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities

Abstract

We survey some of our recent results on inverse problems for evolution equations. The goal is to provide an unified approach to solve various type of evolution equations. The inverse problems we consider consist in determining unknown 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 and boundary lower order coefficients in wave and heat equations. Some of the results presented here are slightly improved from their original versions.