Inverse moving point source problem for the wave equation

Hanin Al Jebawy (1) , Abdellatif El Badia (1) , Faouzi Triki (2)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne
2 EDP - Equations aux Dérivées Partielles

In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different points of the boundary over a finite time interval is sufficient to determine uniquely its trajectory. We also derive a Lipschitz stability estimate for the inversion.

Mots clés: Inverse source problem; Moving source; Wave equation

Domaines: Mathématiques [math]

Hanin Al Jebawy, Abdellatif El Badia, Faouzi Triki. Inverse moving point source problem for the wave equation. 2022. ⟨hal-03607257⟩