Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 88, pp. 1-13.

Title: Existence of global solutions to reaction-diffusion systems with
       nonhomogeneous boundary conditions via a Lyapunov functional
        
Author: Said Kouachi (Centre Univ. Tebessa, Algerie)
         
Abstract: 
 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