Sharp estimates on minimum travelling wave speed of reaction diffusion systems modelling autocatalysis

摘要

This article studies propagating wave fronts in an isothermal chemical reaction A + 2B -> 3B involving two chemical species, a reactant A and an autocatalyst B, whose diffusion coefficients, D-A and D-B, are unequal due to different molecular weights and/or sizes. Explicit bounds v(*) and v* that depend on D-B/D-A are derived such that there is a unique travelling wave of every speed v >= v* and there does not exist any travelling wave of speed v < v*. New to the literature, it is shown that v(*) proportional to v* proportional to D-B/D-A when D-B <= D-A. Furthermore, when D-A <= D-B, it is shown rigorously that there exists a v(min) such that there is a travelling wave of speed v if and only v >= v(min). Estimates on v(min) significantly improve those of early works. The framework is built upon general isothermal autocatalytic chemical reactions A + nB -> (n + 1)B of arbitrary order n >= 1.