Approximation of blowing UP solutions to semilinear parabolic equations using "mass controlled" parabolic systems

Mathematical Models and Methods in Applied Sciences

Volumn 9, Issue 7, 1999, Pages 1077-1088

  Fayyad, D ^a   Nassif, N ^b  

^a LEBANESE UNIVERSITY   (Lebanon)

^b UNIVERSITÉ DE REIMS CHAMPAGNE ARDENNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033442031     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202599000488     Document Type: Article

References (15)

1. J. Bebernes and D. Eberley, Mathematical Problems from Combustion Theory (Springer-Verlag, 1989), p. 83.
2. H. Brezis, Analyse Fonctionnelle (Masson, 1983).
3. J. Bebernes and D. Kassoy, A mathematical analysis of blow-up for thermal runaway, SIAM J. Appl. Math. 40 (1981) 476-484.
4. M. Escobedo and M. A. Herrero, Boundedness and blow up for a semilinear reaction diffusion system, J. Differential Equations 89 (1991) 176-202.
5. M. Escobedo, Explosion et existence globale pour un système faiblement couplé d'équations de réaction-diffusion, manuscript.
6. D. Fayyad and N. Nassif, On the approximation of single blow-up time for semilinear parabolic equations. Parts I and II. Publication du Laboratoire de Mathématiques de l'Université de Reims, URA 1890.
7. D. Fayyad and N. Nassif, Numerical Blow up times approximations to single-point blow up semilinear parabolic equations, manuscript.
8. A. Friedman and B. MacLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. J. Math. 34 (1985) 425-477.
9. v, Bull. Amer. Math. Soc. 75 (1969) 132-135.
10. M. Pierre and D. Schmitt, Global existence for a reaction-diffusion system with a balanced law, in Proc. of the Conference on Semigroups of Operators and Applications, Curacao, August (1992).
11. M. Pierre and D. Schmitt, Blow-up in reaction-diffusion systems with dissipation of mass. Rapport INRIA, 2652 (1995).
12. D. Schmitt, Existence globale ou explosion pour les systems de reaction-diffusion avec contrle de masse, Thesis, Universite de Nancy (1995).
13. p, Indiana Univ. J. Math. 29 (1980) 79-102.
14. F. Weissler, Existence and non-existence of global solutions for a semilinear heat equation, Israel J. Math. 38 (1981) 29-40.
15. F. Weissler, Single point blow-up for a semilinear initial value problem, J. Differential Equation 55 (1984) 204-224.