Front form and velocity in a one-dimensional autocatalyticA+B→2Areaction

We consider the general irreversible $A+B\to 2A$ autocatalytic reaction in one dimension, for which the corresponding diffusion constants $D_A$ and $D_B$ may differ. Contrary to mean-field-type predictions, the Monte Carlo simulations show that, as long as $D_A>0,$ only a unique, stable front propagates with constant velocity. When $D_A=0\mathrm{}$ the behavior changes drastically: both the front’s position and its characteristic width grow with $t^{1/2}.$ These findings are adequately described within a Smoluchowski-type approach.