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

This issue Previous Article Periodic solutions to nonlocal MEMS equations Next Article Degenerate flux for dynamic boundary conditions in parabolic and hyperbolic equations

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: February 2015

Revised: September 2015

Published: June 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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