On the identification of the nonlineari...

We consider an undetermined coefficient inverse problem for a nonlinear 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  \kappa 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 \Sigma  representing the receiving transducer array. After an analysis of the map from  \kappa  to the overposed data, we show injectivity of its linearisation and use this as motivation for several iterative schemes to recover \kappa. Numerical simulations will also be shown to illustrate the efficiency of the methods.