Blow-up for Semidiscretizations of some Semilinear Parabolic Equations with a Convection Term

This paper concerns the study of the numerical approximation for the following parabolic equations with a convection termwhere p > 1.We obtain some conditions under which the solution of the semidiscrete form of the above problem blows up in a finite time and estimate its semidiscrete blow-up time. We also prove that the semidiscrete 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