NUMERICAL SCHEME FOR SOLVING SOME REACTION DIFFUSION EQUATIONS WITH BLOW UP

Geneviève Barro-Kabre (Burkina Faso), Ousséni So (Burkina Faso), Ousseynou Nakoulima (France) and Blaise Some (Burkina Faso)

Received September 30, 2007

References:

[1] H. Amann, On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana Univ. Math. J. 21 (1971), 125. [2] Geneviève Barro, Contribution à la résolution numérique de quelques problèmes de réaction diffusion non linéaires, Thèse de Doctorat Unique, Université de Ouagadougou, 2005. [3] Geneviève Barro, Benjamin Mampassi, Longin Somé, Jean Marie Ntaganda, Ousséni So and Blaise Somé, Full discretization of some reaction diffusion equation with blow up, Central European Journal of Mathematics 4(2) (2006), 260-269. [4] H. Brezis, Analyse Fonctionnelle, Théorie et Applications, Masson, Paris, 1983. [5] H. Brezis and Augusto C. Ponce, Remarks on the strong maximum principle, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, B.C. 187 and Rutgers University, 110 Frelinghuysen Rd., NJ, 08854. Volume 16, Number 1, January 2003, pp. 1-12. [6] H. Brezis and M. Sibony, Méthode d'approximation et d’itération pour les opérateurs monotonnes, Archives for Rational Mechanics and Analysis 41(4) (1979). [7] M. Chlebik and M. Fila, Blow-up of positive solutions of a semilinear parabolic equation with a gradient term, Dyn. Contin. Discrete Impulsive Syst. 10 (2003), 525-537. [8] A. Frieman and B. McLeod, Blow up of solutions of nonlinear degenerate parabolic equations, Arch. Rational Mech. Anal. 96 (1986), 55-80. [9] V. A. Galaktionov and J. L. Vàzquez, The problem of blow-up in nonlinear parabolic equations, Discrete Continuous Dynamical Systems 8(2) (2002), 399-433. [10] M. N. LeRoux, Numerical solution of a fast diffusion equation, J. Math. Anal. Appl. 137 (1989), 354-370. [11] M. N. LeRoux, Semidiscretization in time of nonlinear parabolic equations with blow up of the solution, SIAM J. Numer. Anal. 31 (1994), 170-195. [12] M. N. LeRoux, Numerical solution of fast or slow diffusion equations, J. Comput. Appl. Math. 97 (1998), 121-136. [13] M. N. LeRoux and H. Wilhelmsson, Simultaneous diffusion, reaction and radiative loss processes in plasmas: numerical analysis with application to the dynamics of a fusion reactor plasma, Phys. Scripta 45 (1992), 188-192. [14] P. E. Sacks, Global behavior for a class of nonlinear evolution equations, SIAM J. Math. Anal. 16 (1985), 233-250. [15] J. Simon, Compact sets in the space Ann. Mat. Pura Appl. 146 (1987), 65-96.

Keywords and phrases: reaction diffusion equation, nonlinear parabolic problems, blow-up.