# American Institute of Mathematical Sciences

May  2007, 1(2): 229-245. doi: 10.3934/ipi.2007.1.229

## Integral equations for inverse problems in corrosion detection from partial Cauchy data

 1 Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716-2553, United States 2 Institute für Numerische und Angevandte Mathematik, Universität Göttingen, Germany

Received  August 2006 Revised  October 2006 Published  April 2007

We consider the inverse problem to recover a part $\Gamma_c$ of the boundary of a simply connected planar domain $D$ from a pair of Cauchy data of a harmonic function $u$ in $D$ on the remaining part $\partial D\setminus \Gamma_c$ when $u$ satisfies a homogeneous impedance boundary condition on $\Gamma_c$. Our approach extends a method that has been suggested by Kress and Rundell [17] for recovering the interior boundary curve of a doubly connected planar domain from a pair of Cauchy data on the exterior boundary curve and is based on a system of nonlinear integral equations. As a byproduct, these integral equations can also be used for the problem to extend incomplete Cauchy data and to solve the inverse problem to recover an impedance profile on a known boundary curve. We present the mathematical foundation of the method and illustrate its feasibility by numerical examples.
Citation: Fioralba Cakoni, Rainer Kress. Integral equations for inverse problems in corrosion detection from partial Cauchy data. Inverse Problems & Imaging, 2007, 1 (2) : 229-245. doi: 10.3934/ipi.2007.1.229
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