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In this paper we consider the blow-up for solutions to a weakly coupledsystem of semilinear damped wave equations of derivative type in the scatteringcase. After introducing suitable functionals proposed by Lai-Takamura for thecorresponding single semilinear equation, we employ Kato's lemma to derive theblow-up result in the subcritical case. On the other hand, in the critical casean iteration procedure based on the slicing method is employed. Let us pointout that we find as critical curve in the p-q plane for the pair of exponents(p, q) in the nonlinear terms the same one as for the weakly coupled system ofsemilinear not-damped wave equations with the same kind of nonlinearities.

Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case