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Zbl 1139.45003
Ivanyshyn, Olha; Kress, Rainer
Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks.
(English)
[J] J. Integral Equations Appl. 18, No. 1, 13-38 (2006). ISSN 0897-3962

Authors' summary: For the problem to determine the shape of a perfectly conducting inclusion within a conducting homogeneous host medium from overdetermined Cauchy data on the accessible exterior boundary, that is, for an inverse Dirichlet boundary value problem, recently {\it R. Kress} and {\it W. Rundell} [Inverse Probl. 21, No. 4, 1207--1223 (2005; Zbl 1086.35139)] suggested a new inverse algorithm based on nonlinear integral equations arising from the reciprocity gap principle. The present paper extends this approach to the case of a perfectly insulating inclusion and the case of a perfectly conducting crack. The mathematical foundations of these extensions are provided and numerical examples illustrate the feasibility of the method.
MSC 2000:
*45G10 Nonsingular nonlinear integral equations
47G10 Integral operators
35J05 Laplace equation, etc.
35R30 Inverse problems for PDE

Keywords: inverse Dirichlet boundary value problem; inverse algorithm; nonlinear integral equations; insulating inclusion; conducting crack; numerical examples

Citations: Zbl 1086.35139

Cited in: Zbl 1253.45005

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