Global existence of solutions for an m­-component reaction-diffusion system with a tridiagonal ­2-Toeplitz diffusion matrix and polynomially growing reaction terms

Abdelmalek, Salem; Bendoukha, Samir

Global existence of solutions for an m-component reaction-diffusion system with a tridiagonal 2-Toeplitz diffusion matrix and polynomially growing reaction terms

Document Type : Original Article

Authors

Salem Abdelmalek ¹
Samir Bendoukha ²

¹ Department of mathematics, University of Tebessa 12002 Algeria.

² Electrical Engineering Department, College of Engineering at Yanbu, Taibah University, Saudi Arabia.

Abstract

This paper is concerned with the local and global existence of solutions for a generalized m-component
a reaction-diffusion system with a tridiagonal 2-Toeplitz diffusion matrix and polynomial growth. We derive
the eigenvalues and eigenvectors and determine the parabolicity conditions in order to diagonalize the
proposed system. We, then, determine the invariant regions and utilize a Lyapunov functional to establish
the global existence of solutions for the proposed system. A numerical example is used to illustrate and
conrm the findings of the study.

Keywords

References

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Communications in Nonlinear Analysis