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

Abstract

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 , which complements the uniqueness results obtained by Trofimchuk et al.