Identifiability of some space dependent coefficients in a wave equation of nonlinear acoustics. (English) Zbl 1540.35468
Summary: 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.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 76Q05 | Hydro- and aero-acoustics |
Keywords:
nonlinearity parameter tomography; Jordan-Moore-Gibson-Thompson (JMGT) equation; nonlinear acousticsReferences:
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