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

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  • Salem Abdelmalek1,
  • Samir Bendoukha2,
  1. Department of mathematics, University of Tebessa 12002 Algeria.
  2. Electrical Engineering Department, College of Engineering at Yanbu, Taibah University, Saudi Arabia.

Published in Issue 2025-11-09

How to Cite

Global existence of solutions for an m­-component reaction-diffusion system with a tridiagonal ­2-Toeplitz diffusion matrix and polynomially growing reaction terms. (2025). Communications in Nonlinear Analysis, 3(1). https://oiccpress.com/cna/article/view/17892

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Abstract

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

Keywords

  • Reaction-diffusion systems,
  • invariant regions,
  • diagonalization,
  • global existence,
  • Lyapunov functional
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References

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