Uniqueness of some space dependent coefficients in a wave equation of nonlinear acoustics

Barbara Kaltenbacher

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arXiv · 2305.04110

Uniqueness of some space dependent coefficients in a wave equation of nonlinear acoustics

Barbara Kaltenbacher

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Abstract

In this paper we prove uniqueness for some parameter identification problems for the JMGT equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients to be recovered are the space dependent nonlinearity parameter, sound speed, and attenuation parameter, and the observation available is a single time trace of the acoustic pressure on the boundary. This is a setting relevant to several ultrasound based tomography methods. Our approach relies on the Inverse Function Theorem, which requires to prove that the forward operator is a differentiable isomorphism in appropriately chosen topologies and with an appropriate choice of the excitation.

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Barbara Kaltenbacher. 2023-05-06. Uniqueness of some space dependent coefficients in a wave equation of nonlinear acoustics. https://arxiv.org/abs/2305.04110

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