Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term

This paper deals with the blow-up phenomena for a nonlinear pseudo-parabolic equation with a memory term u(t) - Delta u - Delta u(t) + integral(t)(0) g(t - tau)Delta u(tau)d tau = vertical bar u vertical bar(p)u in a bounded domain, with the initial and Dirichlet boundary conditions. We first obtain the finite time blow-up results for the solutions with initial data at non-positive energy level as well as arbitrary positive energy level, and give some upper bounds for the blow-up time T* depending on the sign and size of initial energy E(0). In addition, a lower bound for the life span T* is derived by means of a differential inequality technique if blow-up does occur.