Journal of Applied Mathematics
Volume 2007 (2007), Article ID 12375, 15 pages
doi:10.1155/2007/12375
Research Article
Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Tridiagonal Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions
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.
Abstract
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.