Unique determination of a time-dependent potential for wave equations from partial data

Yavar Kian (1)

1 CPT - Centre de Physique Théorique - UMR 7332

We consider the inverse problem of determining a time-dependent coefficient of order zero q, appearing in a wave equation ∂ 2 t u − ∆u + q(t, x)u = 0 in Q = (0, T) × Ω with Ω a C 2 bounded domain of R n , n 2, from partial observations of the solutions on ∂Q. Using suitable geometric optics solutions and Carleman estimates, we prove global unique determination of a coefficient q ∈ L ∞ (Q) from these observations .

Mots clés: Inverse problems; wave equation; scalar time-dependent potential; Carleman estimates; partial data Mathematics subject classification 2010 : 35R30; 35L05

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian. Unique determination of a time-dependent potential for wave equations from partial data. 2015. ⟨hal-01154831v1⟩