Bounds for blow-up time in a semilinear parabolic problem with viscoelastic term

We consider a semilinear parabolic equation with viscoelastic term u(t) - Delta u + integral(t)(0) g(t - s)Delta u(x, s)ds = |u|(p-2)u. By the means of differential inequality technique, we obtain a lower bound for blow-up time of the solution if blow-up occurs. At the same time, we establish a new blow-up criterion and give an upper bound for blow-up time of the solution under some conditions on p, g and u(0). (C) 2017 Elsevier Ltd. All rights reserved.