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

Salem, Abdelmalek

doi:https://doi.org/10.1155/2007/12375

Journal of Applied Mathematics

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Research Article | Open Access

Volume 2007 | Article ID 012375 | https://doi.org/10.1155/2007/12375

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

Abdelmalek Salem¹

Academic Editor: Bernard Geurts

Received04 Jun 2007

Accepted28 Sept 2007

Published31 Dec 2007

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.

References

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Copyright

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.

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