Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 68, pp. 1-10.

Title: Existence of global solutions to reaction-diffusion systems via 
       a Lyapunov functional
   
Author: Said Kouachi (Centre universitaire de Tebessa, Algerie)
         
Abstract:  
  The purpose of this paper is to construct polynomial functionals
  (according to solutions of the coupled reaction-diffusion equations)
  which give $L^{p}$-bounds for solutions. When the
  reaction terms are sufficiently regular, using the well known
  regularizing effect, we deduce the existence of global solutions.
  These functionals are obtained independently of work done by
  Malham and Xin [11].

Submitted May 29, 2001. Published October 23, 2001.
Math Subject Classifications: 35K45, 35K57.
Key Words: Reaction-diffusion systems; global existence; Lyapunov functional.