Blow-up for coupled nonlinear wave equations with damping and source

We consider the system of nonlinear wave equations {utt+ut+|ut|m−1ut=div(ρ1(|∇u|2)∇u)+f1(u,v),(x,t)∈Ω×(0,T),vtt+vt+|vt|r−1vt=div(ρ2(|∇v|2)∇v)+f2(u,v),(x,t)∈Ω×(0,T), with initial and Dirichlet boundary conditions. Under some suitable assumptions on the functionsf1, f2f2, ρ1ρ1, ρ2ρ2, parameters r,mr,m and the initial data, the result on blow-up of solutions and upper bound of blow-up time are given.