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The aim of this paper is to construct invariant regions of a generalizedm-component reaction-diffusion system with a tri-diagonal Toeplitz matrix ofdiffusion coefficients and prove the global existence of solutions usingLyapunov functional. The paper assumes nonhomogeneous boundary conditions andpolynomial growth for the non-linear reaction term.

Existence of Global Solutions Via Invariant Regions for a Generalized  Reaction-Diffusion System with a Tri-diagonal Toeplitz Matrix of Diffusion  Coefficients