Most publications on reaction-diffusion systems of components () impose inequalities to the reaction terms, to prove existence of global solutions (see Martin and Pierre  and Hollis ). The purpose of this paper is to prove existence of a global solution using only one inequality in the case of 3 component systems. Our technique is based on the construction of polynomial functionals (according to solutions of the reaction-diffusion equations) which give, using the well known regularizing effect, the global existence. This result generalizes those obtained recently by Kouachi  and independently by Malham and Xin .
Submitted December 13, 2001. Published October 16, 2002.
Math Subject Classifications: 35K45, 35K57.
Key Words: Reaction diffusion systems, Lyapunov functionals, global existence
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|Said Kouachi |
Centre Univ. Tebessa, Dept. Mathematiques,
12002, Tebessa, Algerie
Lab. Mathemathiques, Universite d'Annaba,
B. P. 12, Annaba, 23200, Algerie
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