Bounds for blow-up time of a reaction–diffusion equation with weighted gradient nonlinearity

Abstract

In this paper, we focus on the bounds for blow-up time of null Dirichlet initial boundary value problem for a reaction–diffusion equation with weighted gradient nonlinearity. By virtue of the method of super-sub solution and the technique of modified differential inequality, we establish sufficient conditions to guarantee that the solution blows up at finite time under appropriate measure sense. Meanwhile, upper and lower bounds for the blow-up time are found in higher dimensional spaces and some examples for application are presented.