Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source

In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations utt−Δu+∫0tg1(t−τ)Δu(τ)dτ+|ut|m−1ut=f1(u,v),vtt−Δv+∫0tg2(t−τ)Δv(τ)dτ+|vt|r−1vt=f2(u,v) in Ω×(0,T)Ω×(0,T) with initial and Dirichlet boundary conditions, where ΩΩ is a bounded domain in Rn,n=1,2,3Rn,n=1,2,3. Under suitable assumptions on the functions gi(⋅)gi(⋅), fi(⋅,⋅)(i=1,2), the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property.