Abstract
•An identifiability result is established for Helmholtz point sources identification.•First local Lipschitz stability result is obtained from the Gâteaux differentiability.•Second local Lipschitz stability result is given with explicit stability constant.•A non-iterative numerical algorithm is proposed.•Numerical tests are given to prove the efficiency of the algorithm.
We consider the problem of identification of point sources located in a bounded domain, by performing a single measurement of the Cauchy data on the accessible boundary. An identifiability result is proved for this problem.
A local Lipschitz stability result is established and a numerical inversion algorithm is proposed by using the reciprocity gap concept.