On a singular initial-boundary-value problem for a reaction-diffusion equation arising from a simple model of isothermal chemical autocatalysis

Abstract

In this paper we examine the evolution that occurs when a localized input of an autocatalyst B is introduced into an expanse of a reactant A. The reaction is autocatalytic of order p,so A -> B at rate k [A] [B] p with rate constant k . We examine the case when 0 < p < 1, with p>/ 1 having been examined by Needham & Merkin (Phil. Trans. R. Soc. Lond. A 337, 261—274 (1991)). In particular, we show that the fully reacted state is not achieved (as t-> oo) via the propagation of a travelling wavefront (as for p>/ 1) but is approached uniformly in space as t-00.