Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 141, pp. 1-9.

Title: Existence of global solutions for a system of
       reaction-diffusion equations having a triangular matrix

Author: El Hachemi Daddiouaissa (Univ. Kasdi Merbah, Algeria)

Abstract:
 We consider the system of reaction-diffusion equations
 $$\displaylines{
  u_{t}-a\Delta u=\beta-f(u,v)-\alpha u,\cr
  v_{t}-c\Delta u-d\Delta v=g(u,v)-\sigma v.
 }$$
 Our aim is to establish the existence of global classical solutions
 using the method used by Melkemi, Mokrane, and Youkana [19].
 
Submitted August 19, 2007. Published October 16, 2008.
Math Subject Classifications: 35K57, 35K45.
Key Words: Reaction-diffusion systems; Lyapunov functional; global solution.