Recovering coefficients in a system of semilinear Helmholtz equations from internal data
Analysis of PDEs
2023-07-06 v1 Numerical Analysis
Numerical Analysis
Optimization and Control
Abstract
We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We derive results on the uniqueness and stability of the inverse problem in the case of small boundary data based on the technique of first- and higher-order linearization. Numerical simulations are provided to illustrate the quality of reconstructions that can be expected from noisy data.
Keywords
Cite
@article{arxiv.2307.01385,
title = {Recovering coefficients in a system of semilinear Helmholtz equations from internal data},
author = {Kui Ren and Nathan Soedjak},
journal= {arXiv preprint arXiv:2307.01385},
year = {2023}
}