Stability in the determination of a time-dependent coefficient for wave equations from partial data

Yavar Kian (1, 2)

1 CPT - E8 Dynamique quantique et analyse spectrale
2 CPT - Centre de Physique Théorique - UMR 7332

Let $\Omega$ be a $C^2$ bounded domain of $\mathbb R^n$, $n\geq2$, and fix $Q=(0,T)\times\Omega$ with $T>0$. We consider the stability in the inverse problem of determining a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta_x u+q(t,x)u=0$ in $Q$, from partial observations on $\partial Q$. The observation is given by a boundary operator associated to the wave equation. Using suitable geometric optics solutions and Carleman estimates, we prove a stability estimate in the determination of $q$ from the boundary operator

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian. Stability in the determination of a time-dependent coefficient for wave equations from partial data. Journal of Mathematical Analysis and Applications, 2016, 436 (1), pp.408-428. ⟨10.1016/j.jmaa.2015.12.018⟩. ⟨hal-01011051v3⟩