The problem of detecting corrosion by an electric measurement revisited

Mourad  Choulli; Aymen  Jbalia

doi:10.3934/dcdss.2016018

Article Contents

2016, Volume 9, Issue 3: 643-650. Doi: 10.3934/dcdss.2016018

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The problem of detecting corrosion by an electric measurement revisited

Mourad Choulli^1, and
Aymen Jbalia^2,

1.
Institut Élie Cartan de Lorraine, UMR CNRS 7502, Université de Lorraine-Metz, Boulevard des Aiguillettes, BP 70239, 54506 Vandoeuvre les Nancy cedex, Ile du Saulcy, 57045 Metz cedex 01
2.
Faculté des Sciences de Bizerte, Département des Mathématiques, 7021 Jarzouna Bizerte

Received: January 31, 2015

Revised: August 31, 2015

Published: May 2016

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Abstract

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 [3] 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 local $L^2$-norm at the boundary, of the solution of the boundary value problem used in modeling the problem of detection corrosion by an electric measurement.

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Mathematics Subject Classification: Primary: 35R30.

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