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

TL;DR

This paper presents a unified method using observability inequalities to solve inverse problems for evolution equations, enabling the determination of unknown coefficients from boundary measurements with improved stability and uniqueness results.

Contribution

It introduces a unified framework for inverse problems in evolution equations, leveraging observability inequalities and specific initial conditions for enhanced results.

Findings

Uniqueness and stability estimates for wave and heat equations.

Improved results over previous versions.

Effective recovery of unknown coefficients from boundary data.

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 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.