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- W3136642988 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 nonlocal 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 used to recover it and from this basis develop and analyse Newton-type schemes for its effective recovery." @default.
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- W3136642988 date "2021-03-16" @default.
- W3136642988 modified "2023-09-23" @default.
- W3136642988 title "On an inverse problem of nonlinear imaging with fractional damping" @default.
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