An inverse acoustic scattering problem for an obstacle with an impedance boundary condition
type: Item
instance of: scholarly article
title: An inverse acoustic scattering problem for an obstacle with an impedance boundary condition
zbMATH Open document ID: 0571.35108
DOI: 10.1016/0022-247X(85)90052-6
author: Robert T. Smith
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: This interesting paper is concerned with the two-dimensional inverse problem of plane, time-harmonic wave diffraction by a bounded obstacle on the surface of which an impedance condition is imposed. The aim of the paper is to find a method for determining (approximately) both the shape of the obstacle and the surface impedance from the scattered far field data. Given the low-frequency patterns of the scattered fields resulting from diffraction of three plane waves on the obstacle, the author shows that the problems of determining the scatterer shape and the surface impedance can be isolated and solved successively. In his analysis he uses integral equation methods to represent the scattered field and conformal mapping approach to describe the scatterer shape. He shows the way in which this shape can be determined from the knowledge of the Fourier series expansion of the low-frequency, scattered far field patterns. For the surface impedance the author obtains a Fredholm equation of the first kind. He pays special attention that the problem of finding the impedance be well-posed.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 78A45
zbMATH DE Number: 3910954
zbMATH Keywords: inverse problem
zbMATH Keywords: wave diffraction
zbMATH Keywords: bounded obstacle
zbMATH Keywords: impedance condition
zbMATH Keywords: low-frequency patterns
zbMATH Keywords: integral equation methods
zbMATH Keywords: conformal mapping
zbMATH Keywords: Fourier series
zbMATH Keywords: far field patterns
zbMATH Keywords: Fredholm equation of the first kind
zbMATH Keywords: well-posed
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3910954