Accelerating fronts in autocatalysis

We consider a reaction-diffusion system modelling propagating fronts of an autocatalytic reaction of order m in a one-dimensional, infinitely extended medium. The Lewis number, i.e. the ratio of the molecular diffusivity of t he autocatalyst to that of the reactant, is arbitrary. We prove that if the initial profile of the front decays exponentially or algebraically With ex ponent mu > 1/(m - 1), then the speed of the front is bounded for all times . Our method relies on weighted Lebesgue and Sobolev-space estimates, from which we can reconstruct pointwise results for the decay of the front via i nterpolation. The result gives both a functional analytic foundation, and a n extension to arbitrary Lewis numbers, to the numerical studies of Sherrat t & Marchant and the asymptotic analysis of Needham & Barnes.