Schenkel A., Stubbe J., Wittwer P.
Asymptotics of Solutions in a A+B -> C Reaction-Diffusion System
(219K, postscript)
ABSTRACT. We analyze the long time behavior of an initial value problem
that models a chemical reaction-diffusion process A+B -> C. The problem has
previously been studied by Galfi and Racz [1], who predicted the critical
indices associated with the reaction by using a scaling ansatz motivated by
numerical simulations. In this paper we point out some difficulties which
appear in problems of this type due to the non-uniform convergence of the
solutions towards the scaling limit, and solve them by giving an explicit
description of the corrections to scaling that have to be included to prove
bounds on the solution that are uniform in space and time. This allows us
to relate rigorously the critical exponents as computed from the scaling
ansatz to the exponents of the reaction.