Asymptotics and uniqueness of traveling wavefronts for a delayed model of the Belousov–Zhabotinsky reaction

ABSTRACT

This paper is concerned with asymptotics and uniqueness of traveling wavefronts for a delayed model of the Belousov–Zhabotinsky reaction. It is known that this system admits traveling wavefronts for both monostable and bistable types. In this paper, we further study the monostable case. We first establish the precisely asymptotic behavior of traveling wavefronts with the help of Ikehara's Theorem. Then based on the obtained asymptotic behavior, the uniqueness of the traveling wavefronts is proved by the strong comparison principle and the sliding method, when time delay $h\ne 0$, which complements the uniqueness results obtained by Trofimchuk et al.

KEYWORDS:

• Belousov–Zhabotinsky reaction
• traveling wavefronts
• asymptotic behavior
• uniqueness

AMS SUBJECT CLASSIFICATIONS (2010):

• 34K12
• 35K57
• 92D25

Acknowledgments

I am very grateful to the anonymous referees for their careful reading and helpful suggestions which led to an improvement of my original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author was supported by NSF of China [grant number 11861056] and NSF of Gansu Province [grant number 18JR3RA093].