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- Title
Identifiability of some space dependent coefficients in a wave equation of nonlinear acoustics.
- Authors
Kaltenbacher, Barbara
- Abstract
In this paper we prove uniqueness for some parameter identification problems for the Jordan-Moore-Gibson-Thompson (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.
- Subjects
NONLINEAR acoustics; NONLINEAR wave equations; SOUND pressure; SPEED of sound; PARAMETER identification; INVERSE functions
- Publication
Evolution Equations & Control Theory, 2024, Vol 13, Issue 2, p1
- ISSN
2163-2480
- Publication type
Article
- DOI
10.3934/eect.2023052