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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 1 (January 2021)   > Article

Invariant regions and existence of global solutions to a generalized m-component reaction-diffusion system with tridiagonal symmetric Toeplitz diffusion matrix

Régions invariantes et existence globale de solutions pour un système de réaction-diffusion généralisé à m-composants avec une matrice de diffusion tridiagonale de Toeplitz symétrique

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Karima Abdelmalek
University of Tebessa
Algeria

Belgacem Rebiai
University of Tebessa
Algeria

Salem Abdelmalek
University of Tebessa
Algeria



Published on 5 January 2021   DOI : 10.21494/ISTE.OP.2020.0579

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The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with tridiagonal symmetric Toeplitz diffusion matrix and nonhomogeneous boundary conditions and polynomial growth for the nonlinear reaction terms. Using the eigenvalues and eigenvectors of the diffusion matrix and the parabolicity conditions. So we prove the global existence of solutions using Lyapunov functional.

The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with tridiagonal symmetric Toeplitz diffusion matrix and nonhomogeneous boundary conditions and polynomial growth for the nonlinear reaction terms. Using the eigenvalues and eigenvectors of the diffusion matrix and the parabolicity conditions. So we prove the global existence of solutions using Lyapunov functional.

Reaction-diffusion system invariant regions diagonalization global solution Lyapunov functional

Reaction-diffusion system invariant regions diagonalization global solution Lyapunov functional



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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 1 (January 2021)   > Article