Electron. J. Diff. Eqns., Vol. 2002(2002), No. 88, pp. 1-13.

Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a Lyapunov functional

Said Kouachi

Most publications on reaction-diffusion systems of $m$ components ($m\geq 2$) impose $m$ 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
Lab. Mathemathiques, Universite d'Annaba,
B. P. 12, Annaba, 23200, Algerie
e-mail: kouachi.said@caramail.com

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