On a finite difference scheme for blow up solutions for the Chipot–Weissler equation

In this paper, we are interested in the numerical analysis of blow up for the Chipot–Weissler equation ut=Δu+|u|p−1u−q|∇u|ut=Δu+|u|p−1u−|∇u|q with Dirichlet boundary conditions in bounded domain when p   > 1 and 1≤q≤2pp+1. To approximate the blow up solution, we construct a finite difference scheme and we prove that the numerical solution satisfies the same properties of the exact one and blows up in finite time.