Said Kouachi
Abstract:
Most publications on reaction-diffusion systems of
components
(
)
impose
inequalities to the reaction terms,
to prove existence of global solutions
(see Martin and Pierre [10] and Hollis [4]).
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 [6] and independently by Malham
and Xin [9].
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 and Lab. Mathemathiques, Universite d'Annaba, B. P. 12, Annaba, 23200, Algerie e-mail: kouachi.said@caramail.com |
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