On global existence and nonexistence of solutions to a quasi-linear wave equation with memory, nonlinear damping and source terms

Abstract

In this paper, we consider a quasi-linear wave equation with memory, nonlinear source and damping termsutt−Δut−∑i=1n∂∂xiσi(uxi)+∫0tm(t−s)Δuds+f(ut)=g(u).Under some polynomial growth conditions on the nonlinear functions σi(i=1,2,…,n), f and g, we obtain existence results using Galerkin and monotonicity methods. We also obtain finite time blow up result using the perturbed energy technique.