Determining the potential in a wave equation without a geometric condition. Extension to the heat equation

Kais Ammari (1) , Mourad Choulli (2) , Faouzi Triki (3)

1 FSM - Faculté des Sciences de Monastir
2 IECL - Institut Élie Cartan de Lorraine
3 EDP - Equations aux Dérivées Partielles

We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work is that no geometric condition is imposed to the sub-boundary where the measurements are made. Our results improve those obtained by the first and second authors in [2]. We also show how the analysis for the wave equation can be adapted to an inverse coefficient problem for the heat equation

Mots clés: inverse problem; wave equation; boundary measurements; potential

Domaines: Equations aux dérivées partielles [math.AP]

Kais Ammari, Mourad Choulli, Faouzi Triki. Determining the potential in a wave equation without a geometric condition. Extension to the heat equation. Proceedings of the American Mathematical Society, 2016, 144, pp.4381-4392. ⟨10.1090/proc/13069⟩. ⟨hal-01206417⟩