On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements

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