An inverse problem for the fractionally damped wave equation

We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging and we show the forward problem is locally well posed. We prove that the smooth coefficient of the nonlinearity can be uniquely determined, based o...

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Published inJournal of spectral theory Vol. 15; no. 2; pp. 729 - 750
Main Authors Li, Li, Zhang, Yang
Format Journal Article
LanguageEnglish
Published 01.01.2025
Online AccessGet full text
ISSN1664-039X
1664-0403
DOI10.4171/jst/559

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Abstract We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging and we show the forward problem is locally well posed. We prove that the smooth coefficient of the nonlinearity can be uniquely determined, based on the knowledge of the source-to-solution map and a priori knowledge of the coefficient, in an arbitrarily small subset of the domain. Our approach relies on a second order linearization as well as the unique continuation property of the spectral fractional Laplacian.
AbstractList We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging and we show the forward problem is locally well posed. We prove that the smooth coefficient of the nonlinearity can be uniquely determined, based on the knowledge of the source-to-solution map and a priori knowledge of the coefficient, in an arbitrarily small subset of the domain. Our approach relies on a second order linearization as well as the unique continuation property of the spectral fractional Laplacian.
Author Zhang, Yang
Li, Li
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Snippet We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging and we...
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