Nonlinear acoustic imaging with damping

2023/02/27 by Zhang, Yang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.14174

Abstract

In this paper, we consider an inverse problem for a nonlinear wave equation with a damping term and a general nonlinear term. This problem arises in nonlinear acoustic imaging and has applications in medical imaging and other fields. The propagation of ultrasound waves can be modeled by a quasilinear wave equation with a damping term. We show the boundary measurements encoded in the Dirichlet-to-Neumann map (DN map) determine the damping term and the nonlinearity at the same time. In a more general setting, we consider a quasilinear wave equation with a one-form (a first-order term) and a general nonlinear term. We prove the one-form and the nonlinearity can be determined from the DN map, up to a gauge transformation, under some assumptions.

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