Nonlinear acoustic imaging with damping

TL;DR

This paper investigates an inverse problem for a nonlinear wave equation with damping, demonstrating that boundary measurements can uniquely determine the damping and nonlinear terms, with applications in nonlinear acoustic imaging.

Contribution

It establishes the simultaneous identifiability of damping and nonlinear terms from boundary data in a quasilinear wave equation setting, extending previous results to more general nonlinearities.

Findings

Boundary measurements determine damping and nonlinearity.

Unique recovery of damping and nonlinear terms up to gauge.

Applicability to nonlinear acoustic imaging.

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.