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

In this paper, we consider a quasi-linear wave equation with memory, nonlinear source and damping terms u(tt) - Delta ut - Sigma(n)(i=1) partial derivative/partial derivative x(i) integral(t)(0) m(t - s)uds + f (ut ) = g(u) Under some polynomial growth conditions on the nonlinear functions Sigma i (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. (c) 2021 The Author. Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative. This is an open access article under the CC BY licens ( http://creativecommons.org/licenses/by/4.0/ )