Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]