Traveling waves for a Belousov–Zhabotinsky reaction–diffusion system with nonlocal effect. (April 2022)

• Record Type: Journal Article
• Authors: Han, Bang-Sheng; Chang, Meng-Xue; Bo, Wei-Jian
• Is Part Of: Nonlinear analysis. Volume 64(2022)
• Publication Date: 2022-04
• Subjects: Belousov–Zhabotinsky reaction -- Nonlocal effect -- Traveling wave solutions -- Critical speed; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103423
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is to consider the traveling wave solutions of a Belousov–Zhabotinsky reaction–diffusion system with nonlocal nonlinearity. By combining the super- and sub-solutions and Schauder's fixed point theorem, we first establish the existence and non-existence of traveling wave solutions connecting ( 0, 0 ) to an unknown positive steady state, which is independent of the intensity of nonlocality. Our results indicate that there is a critical speed c ∗ > 0 such that the traveling wave solution exists if c > c ∗, while the traveling wave solution does not exist if c < c ∗ . It is worth noting that the nonlocal effect has a great influence on the final state of traveling wave solutions at + ∞ .