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

Abstract

We consider a semilinear parabolic equation with viscoelastic term ut−△u+∫0tg(t−s)△u(x,s)ds=|u|p−2u.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 u0.