Blow-Up for Discretizations of Some Reaction-Diffusion Equations With a Nonlinear Convection Term

Abstract

This paper concerns the study of the numerical approximation for the following parabolic equations with a nonlinear convection termwhere q ≥ 1 and p ≥ q + 1. We find some conditions under which the solution of the discrete form of the above problem blows up in a finite time and estimate its numerical blow-up time. We also prove that the numerical blow-up time converges to the real one, when the mesh size goes to zero. Finally, we give some numerical experiments to illustrate ours analysis.