Stability for the determination of unknown boundary and impedance with a Robin boundary condition

TL;DR

This paper establishes a logarithmic stability result for an inverse boundary problem related to corrosion detection, enabling the determination of unknown boundary parts and impedance from limited boundary measurements.

Contribution

It provides the first stability estimate of logarithmic type for simultaneously recovering boundary shape and impedance in a corrosion model.

Findings

Logarithmic stability estimate proven for boundary and impedance reconstruction.

Unique determination of the corroded boundary and impedance from two measurements.

Applicable to corrosion detection scenarios with partial boundary data.

Abstract

We consider an inverse problem arising in corrosion detection. We prove a stability result of logarithmic type for the determination of the corroded portion of the boundary and impedance by two measurements on the accessible portion of the boundary.