SHARP ESTIMATES ON MINIMUM TRAVELLING WAVE SPEED SHARP ESTIMATES ON MINIMUM TRAVELLING WAVE SPEED 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, DA and DB, are unequal due to different molecular weights and/or sizes. Explicit bounds v and v that depend on DB/DA 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 ∝ v ∝ DB/DA when DB ≤ DA. Furthermore, when DA ≤ DB, it is shown rigorously that there exists a vmin such that there is a travelling wave of speed v if and only v ≥ vmin. Estimates on vmin 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.