An inverse problem for harmonic acoustics in stratified oceans
type: Item
instance of: scholarly article
title: An inverse problem for harmonic acoustics in stratified oceans
zbMATH Open document ID: 0803.35158
author: R. P. Gilbert
author: Yongzhi Xu
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-09-05T00:00:00Z
full work available at URL: http://purl.umn.edu/1591
review text: The inverse problem of determining the refraction index function \(n(z)\) for acoustic waves in a stratified ocean is under consideration. Thereby it is assumed that the refraction property as well as the propagating sound field, produced by a line source are to be recovered simultaneously. The initial-boundary value problem associated with this applied problem is formulated. Moreover, an equivalent representation of the problem as a nonlinear Volterra integral equation is given. Studying the properties of this integral equation it can be shown that the identification of both unknown functions \(n(z)\) and \(u(r,x)\) (sound pressure) is possible in a unique manner when some additional assumptions on measurement functions are imposed. It would be interesting to make assertions on the stability in order to discuss the well-posedness or ill-posedness in all its aspects.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 399056
zbMATH Keywords: refraction index function
zbMATH Keywords: propagating sound field
zbMATH Keywords: nonlinear Volterra integral equation
reviewed by: Bernd Hofmann
MaRDI profile type: Publication
OpenAlex ID: W1996937247
DOI: 10.1006/JMAA.1993.1203
description: scientific article; zbMATH DE number 399056