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

TL;DR

This paper constructs invariant regions and proves global existence of solutions for multi-component reaction-diffusion systems with specific diffusion matrices, using Lyapunov functionals and invariant region techniques.

Contribution

It introduces a method to establish invariant regions and global solutions for systems with tridiagonal symmetric Toeplitz diffusion matrices, extending previous results.

Findings

Global existence of solutions established

Invariant regions constructed for the system

Applicable to systems with polynomial growth nonlinearities

Abstract

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.