# American Institute of Mathematical Sciences

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August  2014, 19(6): 1769-1781. doi: 10.3934/dcdsb.2014.19.1769

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

 1 Department of Differential Equations, National Technical University, Kyiv 2 Facultad de Ciencias, Universidad de Chile, Santiago, Chile 3 Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca

Received  June 2013 Revised  April 2014 Published  June 2014

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).
Citation: Elena Trofimchuk, Manuel Pinto, Sergei Trofimchuk. On the minimal speed of front propagation in a model of the Belousov-Zhabotinsky reaction. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1769-1781. doi: 10.3934/dcdsb.2014.19.1769
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