The inverse problem for a layered anisotropic half space
type: Item
instance of: scholarly article
title: The inverse problem for a layered anisotropic half space
zbMATH Open document ID: 0970.35159
author: Paul Sacks
author: V. G. Yakhno
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-09-04T00:00:00Z
review text: Considered is the inverse problem of determining the elastic module and density of a medium for a system of partial differential equations of elasticity in a half space \({x\in \mathbb{R}^3; x_3 >0}\). It is assumed that the medium is layered, i.e., the unknown coefficients which characterize the medium are functions of \(x_3\). The additionally symmetry property implies that the module of elasticity is a symmetric matrix, thus there are at most 21 independent elements. The authors consider a special type of anisotropy, cubical with three and hexagonal with five independent elastic modules. The authors prove the possibility of a unique determination of some unknown coefficient functions from measurements of the displacement of the field for \(x\) in the surface \(x_3>0\) and in a finite time interval.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74G75
Mathematics Subject Classification ID: 74J35
zbMATH DE Number: 1246325
zbMATH Keywords: anisotropic elastic media
zbMATH Keywords: coefficient determination
zbMATH Keywords: uniqueness
zbMATH Keywords: partial differential equations of elasticity
reviewed by: Asaf D. Iskenderov
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6137
OpenAlex ID: W1972697628
cites work: Q5638660
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cites work: Q5730679
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cites work: Q3998379
DOI: 10.1006/JMAA.1998.6137
description: scientific article; zbMATH DE number 1246325