Acceleration and reaction–diffusion wavefronts in a simple model for mth-order autocatalysis

Abstract

We consider a simple reaction–diffusion system that models propagating fronts occurring in autocatalytic reactions of order m≥ 1. We obtain results concerning the evolution of reaction–diffusion wavefronts and accelerating wavefronts, which extend to systems those results which have been previously established for an analogous scalar problem. We provide an alternative approach to studying this system (via comparison theorems) to that given by Malham & Oliver in 2000 (using weighted L2 estimates), which enables a considerable extension of the results therein.