INVARIANT REGIONS AND GLOBAL SOLUTIONS FOR REACTION-DIFFUSION SYSTEMS WITH A TRIDIAGONAL SYMMETRIC TOEPLITZ MATRIX OF DIFFUSION COEFFICIENTS

In this article we construct the invariant regions for m-component reaction-diffusion systems with a tridiagonal symmetric Toeplitz matrix of diffusion coefficients and with nonhomogeneous boundary conditions. We establish the existence of global solutions, and use Lyapunov functional methods. The nonlinear reaction term is assumed to be of polynomial growth.