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We would like to study a weakly coupled system of semi-linear classicaldamped wave equations with moduli of continuity in nonlinearities whose powersbelong to the critical curve in the $p-q$ plane. The main goal of this paper isto find out the sharp conditions of these moduli of continuity which classifybetween global (in time) existence of small data solutions and finite timeblow-up of solutions.

The interplay of critical regularity of nonlinearities in a weakly coupled system of semi-linear damped wave equations