Blow-up solutions of a system of nonlinear the Klein-Gordon-Fock Type wave equations

We consider the initial boundary value problem for a system of strongly damped wave equations with homogeneous Dirichlet boundary conditions and a nonlinear source term.By applying a modification of the concavity method, we demonstrate that the solutions blow up for p < 3 with arbitrary positive initial data.Furthermore, we show that the global solvability of the problem for p 3.