Journal of Applied Mathematics
Volume 2007 (2007), Article ID 12375, 15 pages
Research Article

Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Tridiagonal Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions

Abdelmalek Salem

Department of Mathematics and Informatiques, University Center of Tebessa, Tebessa 12002, Algeria

Received 4 June 2007; Accepted 28 September 2007

Academic Editor: Bernard Geurts

Copyright © 2007 Abdelmalek Salem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for reaction-diffusion systems (three equations) with a tridiagonal matrix of diffusion coefficients and with nonhomogeneous boundary conditions after the work of Kouachi (2004) on the system of reaction diffusion with a full 2-square matrix. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth.