  In the present paper, we consider a non self adjoint hyperbolic operator with
a vector field and an electric potential that depend not only on the space
variable but also on the time variable. More precisely, we attempt to stably
and simultaneously retrieve the real valued velocity field and the real valued
potential from the knowledge of Neumann measurements performed on the whole
boundary of the domain. We establish in dimension n greater than two, stability
estimates for the problem under consideration. Thereafter, by enlarging the set
of data we show that the unknown terms can be stably retrieved in larger
regions including the whole domain. The proof of the main results are mainly
based on the reduction of the inverse problem under investigation to an
equivalent and classic inverse problem for an electro-magnetic wave equation.
