Global existence and bounds for blow-up time in a class of nonlinear pseudo-parabolic equations with a memory term

In this article, we consider the initial boundary value problem for a class of nonlinear pseudo-parabolic equations with a memory term:ut-Delta u-a Delta ut+integral 0tg(t-s)Delta u(x,s)ds+bu=Delta pu+k(t)|u|q-2u.Under suitable assumptions, we obtain the local and global existence of the solution by Galerkin method. We prove finite-time blow-up of the solution for initial data at arbitrary energy level and obtain upper bounds for blow-up time by using the concavity method. In addition, by means of differential inequality technique, we obtain a lower bound for blow-up time of the solution if blow-up occurs.