Recovering point sources for the inhomogeneous Helmholtz equation

Gang Bao (1) , Yuantong Liu (1) , Faouzi Triki (2)

1 Zhejiang University
2 EDP - Equations aux Dérivées Partielles

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 Hölder 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.

Domaines: Equations aux dérivées partielles [math.AP]

Gang Bao, Yuantong Liu, Faouzi Triki. Recovering point sources for the inhomogeneous Helmholtz equation. Inverse Problems, 2021, 37 (9), pp.095005. ⟨10.1088/1361-6420/ac164b⟩. ⟨hal-03606719⟩