The mathematical basis of the inverse scattering problem for cracks from near-field data
type: Item
instance of: scholarly article
title: The mathematical basis of the inverse scattering problem for cracks from near-field data
zbMATH Open document ID: 1394.78011
DOI: 10.1155/2015/863086
author: Yao Mao
author: Yongguang Chen
author: Jun Guo
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator's mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator's properties and modified linear sampling method, we reconstruct the shape and surface impedance.
Mathematics Subject Classification ID: 78A46
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 6927424
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/863086
OpenAlex ID: W2115328996
Wikidata QID: Q59119706
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description: scientific article; zbMATH DE number 6927424