Simultaneous determination of wave speed, diffusivity and nonlinearity in the Westervelt equation using complex time-periodic solutions
Analysis of PDEs
2025-09-16 v1 Medical Physics
Abstract
We consider an inverse problem governed by the Westervelt equation with linear diffusivity and quadratic-type nonlinearity. The objective of this problem is to recover all the coefficients of this nonlinear partial differential equation. We show that, by constructing complex-valued time-periodic solutions excited from the boundary time-harmonically at a sufficiently high frequency, knowledge of the first- and second-harmonic Cauchy data at the boundary is sufficient to simultaneously determine the wave speed, diffusivity and nonlinearity in the interior of the domain of interest.
Cite
@article{arxiv.2509.10718,
title = {Simultaneous determination of wave speed, diffusivity and nonlinearity in the Westervelt equation using complex time-periodic solutions},
author = {Sebastian Acosta and Benjamin Palacios},
journal= {arXiv preprint arXiv:2509.10718},
year = {2025}
}