Existence and nonexistence of a global solution for coupled nonlinear wave equations with damping and source

We consider the system of nonlinear wave equations {utt+|ut|m−1ut=div(ρ(|∇u|2)∇u)+f1(u,v),(x,t)∈Ω×(0,T),vtt+|vt|r−1vt=div(ρ(|∇v|2)∇v)+f2(u,v),(x,t)∈Ω×(0,T), with initial and Dirichlet boundary conditions. Under some suitable assumptions on the functions f1f1 and f2f2, the initial data and the parameters in the equations, the theorems of global existence and nonexistence are proved.