A parabolic inverse problem with mixed boundary data. Stability estimates for the unknown boundary and impedance

TL;DR

This paper addresses the inverse problem of identifying inaccessible boundary parts of a conductor using thermal measurements, providing stability estimates for the unknown boundary and impedance in a corrosion context.

Contribution

It introduces a logarithmic stability estimate for reconstructing the damaged boundary and impedance with mixed boundary conditions in a corrosion model.

Findings

Logarithmic stability estimate for boundary reconstruction

Effective determination of impedance in corrosion scenarios

Analysis of mixed boundary condition effects

Abstract

We consider the problem of determining an unaccessible part of the boundary of a conductor by mean of thermal measurements. We study a problem of corrosion where a Robin type condition is prescribed on the damaged part and we prove logarithmic stability estimate.