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

We consider the system of nonlinear wave equations View the MathML source{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), Turn MathJax on 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.