Publication: On an inverse problem of nonlinear imag...
Master data
Title: | On an inverse problem of nonlinear imaging with fractional damping |
Subtitle: | |
Abstract: | This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed in the literature and characterised by the inclusion of non-local operators that give power law damping as opposed to the exponential of classical models. The goal is the inverse problem of recovering a spatially dependent coefficient in the equation, the parameter of nonlinearity κ ( x ) \kappa (x) , in what becomes a nonlinear hyperbolic equation with non-local terms. The overposed measured data is a time trace taken on a subset of the domain or its boundary. We shall show injectivity of the linearised map from κ \kappa to the overposed data and from this basis develop and analyse Newton-type schemes for its effective recovery. |
Keywords: |
Publication type: | Article in journal (Authorship) |
Publication date: | 20.09.2021 (Online) |
Published by: |
Mathematics of Computation
Mathematics of Computation
(
American Mathematical Society (AMS);
)
to publication |
Title of the series: | - |
Volume number: | 91 |
Issue: | 333 |
First publication: | Yes |
Version: | - |
Page: | pp. 245 - 276 |
Versionen
Keine Version vorhanden |
Publication date: | 20.09.2021 |
ISBN (e-book): | - |
eISSN: | 1088-6842 |
DOI: | http://dx.doi.org/10.1090/mcom/3683 |
Homepage: | - |
Open access |
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Authors
Barbara Kaltenbacher (internal) | ||||||
William Rundell
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Assignment
Organisation | Address | ||||
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Fakultät für Technische Wissenschaften
Institut für Mathematik
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AT - 9020 Klagenfurt am Wörthersee |
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Research Cluster | No research Research Cluster selected |
Citation index |
Information about the citation index: Master Journal List
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Peer reviewed |
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Publication focus |
Classification raster of the assigned organisational units:
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working groups | No working group selected |
Cooperations
Organisation | Address | ||
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Texas A&M University
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US - TX 77843 College Station |
Research activities
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Publications: | No related publications |
Events: | No related events |
Lectures: | No related lectures |