An inverse problem for the fractionally damped wave equation
Analysis of PDEs
2023-08-01 v1
Abstract
We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth coefficient of the nonlinearity can be uniquely determined, based on the knowledge of the source-to-solution map and a priori knowledge of the coefficient in an arbitrarily small subset of the domain. Our approach relies on a second order linearization as well as the unique continuation property of the spectral fractional Laplacian.
Keywords
Cite
@article{arxiv.2307.16065,
title = {An inverse problem for the fractionally damped wave equation},
author = {Li Li and Yang Zhang},
journal= {arXiv preprint arXiv:2307.16065},
year = {2023}
}