Stability for an inverse flux and an inverse boundary coefficient problems

TL;DR

This paper derives stability estimates for inverse flux and boundary coefficient problems, and applies these results to solve an inverse corrosion problem by determining unknown boundary coefficients from accessible boundary measurements.

Contribution

It provides new Lipschitz and logarithmic stability estimates for inverse flux and boundary coefficient problems, enabling solutions to practical corrosion detection issues.

Findings

Established Lipschitz and logarithmic stability estimates.

Applied stability results to inverse corrosion problem.

Demonstrated practical use of stability inequalities in corrosion detection.

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.