Recovering point sources for the inhomogeneous Helmholtz equation
Analysis of PDEs
2021-09-01 v3
Abstract
The paper is concerned with an inverse point source problem for the Helmholtz equation. It consists of recovering the locations and amplitudes of a finite number of radiative point sources inside a given inhomogeneous medium from the knowledge of a single boundary measurement. The main result of the paper is a new H\"{o}lder type stability estimate for the inversion under the assumption that the point sources are well separated. The proof of the stability is based on a combination of Carleman estimates and a technique for proving uniqueness of the Cauchy problem.
Keywords
Cite
@article{arxiv.2104.14991,
title = {Recovering point sources for the inhomogeneous Helmholtz equation},
author = {Gang Bao and Yuantong Liu and Faouzi Triki},
journal= {arXiv preprint arXiv:2104.14991},
year = {2021}
}