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

N'Guessan Koffi; Diabate Nabongo; Toure Kidjegbo Augustin

N'Guessan Koffi UFR SED, Alassane Ouattara University of Bouake, 01 BP V 18 Bouake 01 Côte d'Ivoire
Diabate Nabongo UFR SED, Alassane Ouattara University of Bouake, 01 BP V 18 Bouake 01, Côte d'Ivoire
Toure Kidjegbo Augustin Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, BP 1093 Yamoussoukro, Côte d'Ivoire

Keywords: Burgers' equation, semidiscretizations, discretizations, parabolic equations, convection term, blow-up, blow-up time, convergence.

Abstract

This paper concerns the study of the numerical approximation for the following parabolic equations with a convection term

where 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.

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