Stable determination of the surface impedance of an obstacle by far field measurements

We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements

The problem of detecting corrosion by an electric measurement revisited

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 measuremen

Smoothness dependent stability in corrosion detection

We consider the stability issue for the determination of a linear corrosion in a conductor by a single electrostatic measurement. We established a global log-log type stability when the corroded boundary is simply Lipschitz. We also improve such a result obtaining a global log stability by assuming that the damaged boundary is $C^{1,1}$-smooth

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

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

Stable determination of surface impedance on a rough obstacle by far field data

We treat the stability of determining the boundary impedance of an obstacle by scattering data, with a single incident field. A previous result by Sincich (SIAM J. Math. Anal. 38, (2006), 434-451) showed a log stability when the boundary of the obstacle is assumed to be C^{1,1}-smooth. We prove that, when the obstacle boundary is merely Lipschitz, a log-log type stability still holds.Comment: 13 pages, submitted for publicatio

Inverse Problems in Wave Scattering and Impedance Tomography

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