Critically and degenerately damped systems of nonlinear wave equations with source terms

This article is concerned with the global well-posedness of the critically and degenerately damped system of nonlinear wave equations in a bounded domain Ω ⊂ ℝ n , n = 1, 2, 3, with Dirichlét boundary conditions. The nonlinearities f 1(u, v) and f 2(u, v) act as a strong source in the system. Under some restriction on the parameters in the system we obtain several results concerning the existence of local solutions, global solutions, uniqueness and the blow up in finite time.