On the minimal speed of front propagation in a model of the Belousov-Zhabotinsky reaction

Abstract

In this paper, we answer the question about the existence of the minimal speed of front propagation in a delayed version of the Murray model of the Belousov-Zhabotinsky (BZ) chemical reaction. It is assumed that the key parameter $r$ of this model satisfies $0< r \leq 1$ that makes it formally monostable. By proving that the set of all admissible speeds of propagation has the form $[c_*,+\infty)$, we show here that the BZ system with $r \in (0,1]$ is actually of the monostable type (in general, $c_*$ is not linearly determined). We also establish the monotonicity of wavefronts and present the principal terms of their asymptotic expansions at infinity (in the critical case $r=1$ inclusive).