On the characterization of the Fréchet derivative with respect to a Lipschitz domain of the acoustic scattered field
type: Item
instance of: scholarly article
title: On the characterization of the Fréchet derivative with respect to a Lipschitz domain of the acoustic scattered field
zbMATH Open document ID: 0937.35175
author: Rabia Djellouli
author: C. Farhat
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-12-01T00:00:00Z
review text: The characterization of the Fréchet derivative with respect to a domain of a given obstacle is presented. The results are formulated for acoustic scattering problems with a sound-soft obstacle, a sound-hard obstacle, or lossy boundary conditions. It is assumed that, the shape of the scatter is only Lipschitzian, and that the admissible perturbations are the elements of the space of functions with continuous derivatives in \(\mathbb{R}^3\). The proof of the theorem about the characterization of the derivative of the scattered field with respect to the domain as the solution of a particular direct acoustic problem is based on the validity of the chain rule in infinite-dimensional spaces and the classical trace theorems. The results of this paper can be used for reducing the complexity of the solution of inverse scattering problems by iterative methods.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 78A46
zbMATH DE Number: 1354761
zbMATH Keywords: acoustics
zbMATH Keywords: scattering
zbMATH Keywords: Lipschitz domain
zbMATH Keywords: Fréchet differentiability
zbMATH Keywords: domain derivative
zbMATH Keywords: inverse scattering
reviewed by: István Ecsedi
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6536
OpenAlex ID: W2084078381
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DOI: 10.1006/JMAA.1999.6536
description: scientific article; zbMATH DE number 1354761