On the simultanenous identification of two space dependent coefficients in a quasilinear wave equation
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This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importance from time-trace boundary measurements. Specifically, these are the nonlinearity parameter κ(x) often referred to as B/A in the acoustics literature and the wave speed c_0(x). The determination of the spatial change in these quantities can be used as a means of imaging. We consider identifiability from one or two boundary measurements as relevant in these applications. More precisely, we provide results on local uniqueness of κ(x) from a single observation and on simultaneous identifiability of κ(x) and c_0(x) from two measurements. For a reformulation of the problem in terms of the squared slowness =1/c_0^2 and the combined coefficient =κ/c_0^2 we devise a frozen Newton method and prove its convergence. The effectiveness (and limitations) of this iterative scheme are demonstrated by numerical examples.
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