A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation
Analysis of PDEs
2021-05-07 v1 Numerical Analysis
Numerical Analysis
Abstract
The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be consistent, and the proposed numerical simulations are quite promising.
Cite
@article{arxiv.2105.02665,
title = {A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation},
author = {Pierre Marechal and Walter Simo Tao Lee and Faouzi Triki},
journal= {arXiv preprint arXiv:2105.02665},
year = {2021}
}