Existence of Global Solutions Via Invariant Regions for a Generalized   Reaction-Diffusion System with a Tri-diagonal Toeplitz Matrix of Diffusion   Coefficients
  The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with a tri-diagonal Toeplitz matrix of diffusion coefficients and prove the global existence of solutions using Lyapunov functional. The paper assumes nonhomogeneous boundary conditions and polynomial growth for the non-linear reaction term. 
Salem Abdelmalek
math.AP