On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements
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We consider an undetermined coefficient inverse problem for a non- linear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomography. In particular, we investigate the recovery of the nonlinearity coefficient commonly labeled as B/A in the literature which is part of a space dependent coefficient κ in the Westervelt equation governing nonlinear acoustics. Corresponding to the typical measurement setup, the overposed data consists of time trace measurements on some zero or one dimensional set Σ representing the receiving transducer array. After an analysis of the map from κ to the overposed data, we show injectivity of its linearisation and use this as motivation for several iterative schemes to recover κ. Numerical simulations will also be shown to illustrate the efficiency of the methods.
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