On the uniqueness of the shape of a penetrable, anisotropic obstacle
type: Item
instance of: scholarly article
title: On the uniqueness of the shape of a penetrable, anisotropic obstacle
zbMATH Open document ID: 0978.35098
DOI: 10.1016/S0377-0427(99)00323-4
author: Peter Hähner
published in: Journal of Computational and Applied Mathematics
publication date: 2001-07-15T00:00:00Z
review text: This paper studies the direct and inverse scattering problem for time harmonic waves by an inhomogeneous anisotropic medium. In the first part, the direct problem is studied by a variational approach with nonlocal boundary conditions involving the Dirichlet-Neumann operator. The main tool in the proof of uniqueness of the inverse problem consists of an investigation of the corresponding interior transmission problem. The author combines a contraction argument with the Fredholm theory to show existence and uniqueness of this problem. With the help of special solutions, the technique of Kirsch and Kress leads to uniqueness of the inverse problem.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A46
zbMATH DE Number: 1437660
zbMATH Keywords: anisotropic obstacle
zbMATH Keywords: transmission problem
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
reviewed by: Andreas Kirsch
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00323-4
OpenAlex ID: W2068500236
Wikidata QID: Q127152182
description: scientific article; zbMATH DE number 1437660