Lower bounds for blow-up time in a parabolic problem with a gradient term under various boundary conditions

Abstract

This paper deals with the blow-up phenomena of the solution u of a nonlinear parabolic problem with a gradient nonlinearity and time dependent coefficients. By using techniques based on Sobolev type and differential inequalities, we derive explicit lower bounds for the blow-up time, if blow-up occurs, when different boundary conditions are taken into account.