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 satis es 0 < r 1 that makes it formally monostable. By proving that the set of all admissible speeds of propagation has the form [c ;+1), we show here that the BZ system with r 2 (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 in nity (in the critical case r = 1 inclusive).