On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements

DOI10.3934/ipi.2021020zbMath1472.35453arXiv2102.07608OpenAlexW3132907149MaRDI QIDQ1983440

William Rundell, Barbara Kaltenbacher

Publication date: 10 September 2021

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.07608

zbMATH Keywords

coefficient identificationultrasound imagingnonlinearity parameterWestervelt equationnonlinear acoustics, high intensity ultrasound propagation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Inverse problems for PDEs (35R30) Hydro- and aero-acoustics (76Q05) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Semilinear parabolic equations (35K58) Second-order quasilinear hyperbolic equations (35L72)

Related Items (11)

An Inverse Boundary Value Problem Arising in Nonlinear Acoustics ⋮ An inverse problem for a semi-linear wave equation: a numerical study ⋮ On the simultaneous reconstruction of the nonlinearity coefficient and the sound speed in the Westervelt equation ⋮ Optimization problems for PDEs in weak space-time form. Abstracts from the workshop held March 5--10, 2023 ⋮ Born and inverse Born series for scattering problems with Kerr nonlinearities ⋮ Determining the nonlinearity in an acoustic wave equation ⋮ Nonlinearity parameter imaging in the frequency domain ⋮ On the inverse problem of vibro-acoustography ⋮ Weakly Nonlinear Geometric Optics for the Westervelt Equation and Recovery of the Nonlinearity ⋮ On inverse problems for a strongly damped wave equation on compact manifolds ⋮ On an inverse problem of nonlinear imaging with fractional damping

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