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 a unified approach to solve various types of evo-lution equations. The inverse problems we consider consist in determining unknown coefficients from boundary measurements by varying initial conditions. Based on ob-servability inequalities and a special choice of initial conditions, we provide unique-ness and stability estimates for the recovery of volume and boundary lower order co-efficients in wave and heat equations. Some of the results presented here are slightly improved from their original versions.

Keywords

Evolution equations / Laplace-Beltrami operator / observability inequality / geometric control / initial-to-boundary operator