Global stability of traveling fronts of a diffusion system with the Belousov-Zhabotinskii reaction

Hong-Tao Niu; Hong-Tao Niu

doi:10.3934/math.20241233

AIMS Mathematics

2024, Volume 9, Issue 9: 25261-25283. doi: 10.3934/math.20241233

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Research article

Global stability of traveling fronts of a diffusion system with the Belousov-Zhabotinskii reaction

Hong-Tao Niu ^,

School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, Jiangsu 221018, China

Received: 30 July 2024 Revised: 21 August 2024 Accepted: 23 August 2024 Published: 29 August 2024
MSC : 35K40, 35K57, 35C07

This paper studied the asymptotic stability of traveling fronts of the Belousov-Zhabotinskii (BZ for short) system. Under the condition that the initial perturbation decays as $ |x|\rightarrow \infty $, we came to the conclusion that the traveling fronts were globally exponentially stable. The main method was the super and sub-solutions combined with a squeezing technique.
- global stability,
- Belousov-Zhabotinskii,
- traveling fronts,
- super and sub solutions,
- squeezing technique
Citation: Hong-Tao Niu. Global stability of traveling fronts of a diffusion system with the Belousov-Zhabotinskii reaction[J]. AIMS Mathematics, 2024, 9(9): 25261-25283. doi: 10.3934/math.20241233

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Abstract

This paper studied the asymptotic stability of traveling fronts of the Belousov-Zhabotinskii (BZ for short) system. Under the condition that the initial perturbation decays as $ |x|\rightarrow \infty $, we came to the conclusion that the traveling fronts were globally exponentially stable. The main method was the super and sub-solutions combined with a squeezing technique.

References

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