Existence and stability of traveling wavefronts for a nonlocal delay Belousov–Zhabotinskii system

Abstract

This paper is concerned with the existence and stability of traveling wavefronts for a nonlocal delay Belousov–Zhabotinskii system. We first introduce the new variable and change the two-dimensional system with nonlocal delay into a three-dimensional system without delay. Then the existence of traveling wavefronts is obtained by constructing a pair of suitable super- and sub-solutions and applying Schauder's fixed point theorem. Finally, we establish the exponential stability of traveling wavefronts with large speed by the weighted energy method together with the comparison principle, when the initial perturbation around the traveling wavefront decays exponentially as $x\to -\mathrm{\infty }$, but can be arbitrarily large in other locations.

Keywords:

• Belousov–Zhabotinskii system
• traveling wavefronts
• existence
• stability
• nonlocal delay

2010 AMS Subject Classifications:

• 35K57
• 35C07
• 92D25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by National Natural Science Foundation of China [grant number 11861056], The Natural Science Foundation of Gansu Province [grant numbers 21JR7RA121, 21JR7RA209], and Department of Education of Gansu Province: Youth Doctoral Fund [project number 2021QB-018].