Back to Search
Start Over
On an inverse problem of nonlinear imaging with fractional damping.
- Source :
-
Mathematics of Computation . Jan2022, Vol. 90 Issue 333, p245-276. 32p. - Publication Year :
- 2022
-
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 \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 \kappa to the overposed data and from this basis develop and analyse Newton-type schemes for its effective recovery. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255718
- Volume :
- 90
- Issue :
- 333
- Database :
- Academic Search Index
- Journal :
- Mathematics of Computation
- Publication Type :
- Academic Journal
- Accession number :
- 162731418
- Full Text :
- https://doi.org/10.1090/mcom/3683