  In this work we study the blow-up of solutions of a weakly coupled system of
damped semilinear wave equations in the scattering case with power
nonlinearities. We apply an iteration method to study both the subcritical case
and the critical case. In the subcritical case our approach is based on lower
bounds for the space averages of the components of local solutions. In the
critical case we use the slicing method and a couple of auxiliary functions,
recently introduced by Wakasa-Yordanov, to modify the definition of the
functionals with the introduction of weight terms. In particular, we find as
critical curve for the pair (p, q) of the exponents in the nonlinear terms the
same one as for the weakly coupled system of semilinear wave equations with
power nonlinearities.
