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In this work we determine the critical exponent for a weakly coupled systemof semilinear wave equations with distinct scale-invariant lower order terms,when these terms make both equations in some sense parabolic-like. For theblow-up result the test functions method is applied, while for the globalexistence (in time) results we use L2-L2 estimates with additional L1regularity.

Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part