2020/02/21 by Gang Bao, Bao, Gang, Yuantong Liu +3
Earth and Planetary Sciences · Engineering · Mathematics · #35 #Analysis of PDEs (math.AP) #Electrical and Bioimpedance Tomography #FOS: Mathematics #Geophysical and Geoelectrical Methods #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2002.09187
openalex publication_date 2020/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the inverse problem of recovering simultaneously a potential and a point source in a Shrödinger equation from the associated nonlinear Dirichlet to Neumann map. The uniqueness of the inversion is proved and logarithmic stability estimates are derived. It is well known that the inverse problem of determining only the potential while knowing the source, is ill-posed. In contrast the problem of identifying a point source when the potential is given is well posed. The obtained results show that the nonlinear Dirichlet to Neumann map contains enough information to determine simultaneously the potential and the point source. However recovering a point source imbedded in an unknown background medium becomes an ill-posed inversion.