Front propagation in an autocatalytic reaction-subdiffusion system

Abstract

We discuss the front propagation in the autocatalytic irreversible A+B → 2A reaction under subdiffusion as described by continuous time random walks with a heavy tailed waiting time probability density [Equation Found]. Strong arguments in favor of the following propagation picture are presented:At shorter times the front propagates at a velocity decaying as [Equation Found]. This intermediate asymptotic regime can be described within a framework of continuous reaction-subdiffusion equations. At longer times the front gets atomically sharp and the continuous scheme breaks down. In this regime, the propagation velocity shows a faster decay V α tα-1 than in the continuous regime.