Nonlinear exponential stability of traveling front solutions for a reaction-diffusion system with acidic nitrate-ferroin reaction

Lina Wang; Xiaofan Zhu; Yanxia Wu; Lina Wang; Xiaofan Zhu; Yanxia Wu

doi:10.3934/math.20251056

AIMS Mathematics

2025, Volume 10, Issue 10: 23773-23788. doi: 10.3934/math.20251056

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Research article

Nonlinear exponential stability of traveling front solutions for a reaction-diffusion system with acidic nitrate-ferroin reaction

1.
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, China
2.
School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan, 250014, China

Received: 25 August 2025 Revised: 02 October 2025 Accepted: 11 October 2025 Published: 20 October 2025
MSC : 35B35, 35C07, 35K57, 35Q92

This paper is concerned with the nonlinear exponential stability of traveling front solutions for a reaction-diffusion system with acidic nitrate-ferroin reaction. For diffusion coefficient $ \delta $ near $ 1 $, we first establish the perturbation relationship and precise spatial decay rates of traveling front solutions. Subsequently, in some exponentially weighted spaces, we demonstrate the nonlinear exponential stability of the traveling front solutions with all noncritical speeds $ c > c_{\min} = \frac{2}{\sqrt{\beta+1}} $. This improves the stability results in ^[1], in which the authors obtained the stability of traveling front solutions for $ c > \frac{1}{\sqrt{2\beta}} $.
- traveling front solutions,
- spectral analysis,
- exponentially weighted spaces,
- Evans function,
- exponential stability
Citation: Lina Wang, Xiaofan Zhu, Yanxia Wu. Nonlinear exponential stability of traveling front solutions for a reaction-diffusion system with acidic nitrate-ferroin reaction[J]. AIMS Mathematics, 2025, 10(10): 23773-23788. doi: 10.3934/math.20251056

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Abstract

This paper is concerned with the nonlinear exponential stability of traveling front solutions for a reaction-diffusion system with acidic nitrate-ferroin reaction. For diffusion coefficient $ \delta $ near $ 1 $, we first establish the perturbation relationship and precise spatial decay rates of traveling front solutions. Subsequently, in some exponentially weighted spaces, we demonstrate the nonlinear exponential stability of the traveling front solutions with all noncritical speeds $ c > c_{\min} = \frac{2}{\sqrt{\beta+1}} $. This improves the stability results in ^[1], in which the authors obtained the stability of traveling front solutions for $ c > \frac{1}{\sqrt{2\beta}} $.

References

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