Hölder stability in determining the potential and the damping coefficient in a wave 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 improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an initial-to-boundary operator. We partially modify the arguments in [3] to show that actually we have Hölder stability instead of logarithmic stability.

Mots clés: potential; wave equation; damping coefficient; inverse problem; Hölder stability

Domaines: Equations aux dérivées partielles [math.AP]

Kais Ammari, Mourad Choulli, Faouzi Triki. Hölder stability in determining the potential and the damping coefficient in a wave equation. Journal of Evolution Equations, 2019, 19 (2), pp.305-319. ⟨10.1007/s00028-018-0476-9⟩. ⟨hal-01368691⟩