Critical thresholds for the damped wave system with mixed product-type nonlinearities

In this paper, we study the Cauchy problem for a coupled system of damped wave equations with mixed product-type nonlinearities. We have succeeded in determining the critical curve, formulated in terms of the power exponents of nonlinearities, for the global (in time) existence of small data mild solutions and the nonexistence of global mild solutions. Moreover, the global existence result is established by means of Schauder’s fixed point theorem and Banach’s contraction principle, whereas the nonexistence analysis relies on a new iteration scheme adapted to the product-type structure of nonlinearities. To the best of our knowledge, this work provides the first critical threshold results for such systems.