The problem of detecting corrosion by an electric measurement revisited

Mourad Choulli (1) , Aymen Jbalia (2)

1 IECL - Institut Élie Cartan de Lorraine
2 Faculté des Sciences de Bizerte [Université de Carthage]

We establish a logarithmic stability estimate for the problem of detecting corrosion by a single electric measurement. We give a proof based on an adaptation of the method initiated in \cite{BCJ} for solving the inverse problem of recovering the surface impedance of an obstacle from the scattering amplitude. The key idea consists in estimating accurately a lower bound of the $L^2$-norm, locally at the boundary, of the solution of the boundary value problem used in modeling the problem of detection corrosion by an electric measurement

Mots clés: boundary measurement.; boundary measurement; detecting corrosion; Stability estimate

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Aymen Jbalia. The problem of detecting corrosion by an electric measurement revisited. Discrete and Continuous Dynamical Systems - Series S, 2016, 9 (3), pp.643-650. ⟨10.3934/dcdss.2016018⟩. ⟨hal-00864869v3⟩