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

Abstract

This article studies propagating wave fronts in an isothermal chemical reaction A + 2B - \u3e 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 \u3e = v* and there does not exist any travelling wave of speed v \u3c v*. New to the literature, it is shown that v(*) proportional to v* proportional to D-B/D-A when D-B = v(min). Estimates on v(min) significantly improve those of early works. The framework is built upon general isothermal autocatalytic chemical reactions A + nB - \u3e (n + 1)B of arbitrary order n \u3e = 1

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