Let Ω be a C2  bounded domain of Rn , n ≥ 2, and fix Q = (0, T ) × Ω with T > 0. We consider the inverse problem of determining a time-dependent damping coefficient a and a time- dependent potential q, appearing in a Dirichlet initial-boundary value problem for the damped wave equation ∂_t^2u − ∆xu + a(t, x)∂t u + q(t, x)u = 0 in Q from observations on ∂Q.  Using an approach related to the strategy set for partial  data Calderón problems and based on Carleman estimates, our goal is to reduce as much as possible the information  on ∂Q that  allows to determine general time-dependent coefficients. We consider both results of uniqueness and stability for this problem.

Prof. Yavar Kian received his PhD degree in Applied Mathematics from the University of Bordeaux, France, in 2010. He is currently an Assistant Professor at the University of Aix-Marseille, France. He joined the University of Aix-Marseille on 2011. His current research interests include: inverse problems for different PDEs (parabolic, hyperbolic, Schrödinger and elliptic equations), inverse spectral problems, inverse problems on manifolds, inverse and direct problems for fractional diffusion equations.