All Invariant Regions and Global Solutions for m-component Reaction-Diffusion Systems with a Tridiagonal Symmetric Toeplitz Matrix of Diffusion Coefficients

The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for m-component reaction-diffusion systems with a tridiagonal symmetric toeplitz matrix of diffusion coefficients and with nonhomogeneous boundary conditions. The proposed technique is based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth.