Stability for an inverse flux and an inverse boundary coefficient problems

Abstract

We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Furthermore, we demonstrate how the stability inequalities derived for the inverse boundary coefficient problem can be utilized in solving an inverse corrosion problem. This involves determining the unknown corrosion coefficient on an inaccessible part of the boundary based on measurements taken on the accessible part of the boundary.