Volume 17, Issue 8

In the paper [Eppler and Harbrecht, Control & Cybernetics 34: 203–225, 2005], the authors investigated the identification of an obstacle or void of perfectly conducting material in a two-dimensional domain by measurements of voltage and currents at the boundary. In particular, the reformulation of the given nonlinear identification problem was considered as a shape optimization problem using the Kohn and Vogelius criterion. The compactness of the complete shape Hessian at the optimal inclusion was proven, verifying strictly the ill-posedness of the identification problem. The aim of the paper is to present a similar analysis for the related least square tracking formulations. It turns out that the two-norm-discrepancy is of the same principal nature as for the Kohn and Vogelius objective. As a byproduct, the necessary first order optimality condition are shown to be satisfied if and only if the data are perfectly matching. Finally, we comment on possible consequences of the two-norm-discrepancy for the regularization issue.

In this paper we investigate the identification of the time-dependent perfusion coefficient in the transient bio-heat conduction equation. Apart from the usual initial and Dirichlet/Neumann boundary conditions, in this inverse coefficient identification problem the additional measurement information to render a unique solution is represented by the time history of a heat flux/boundary temperature. Several necessary and sufficient conditions for the existence and uniqueness of the solution are provided.

This paper is devoted to the numerical analysis of inverse problem for abstract elliptic differential equations. The presentation uses the general approximation scheme and is based on C 0 -semigroup theory and a functional analysis approach.

We collect some stability and reconstruction results for two inverse boundary value problems arising in corrosion detection.

The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems. In stead of completing the set of data, the set of discrete sine transforms of the data is completed. This is achieved by solving systems of linear equations that have, upon choosing appropriate parameters, positive definite coefficient matrices. Numerical examples are presented.

This paper discusses the inverse problem of determining a spacewise dependent heat source in one-dimensional heat equation in a half infinite domain where data is given at some fixed time. The problem is ill-posed, i.e., the solution, if existing, does not depend continuously on the data. Two regularization solutions of the inverse problem will be given by a simplified Tikhonov regularization method and a modified regularization method. For two regularization solutions, the Hölder type error estimates between the regularization solutions and the exact solution are obtained, respectively. Numerical examples show that two regularization methods are effective for identifying the heat source.