Numerical analysis of reversible A + B <-> C reaction-diffusion systems

TL;DR

This paper introduces a numerical method to analyze large-time behavior of reversible reaction-diffusion systems, revealing complex asymptotic zones and nonmonotonic concentration profiles with potential negative reaction rates.

Contribution

The authors develop a new numerical approach for studying large-time dynamics of reversible reaction-diffusion systems with separated initial reactants.

Findings

Identification of three types of asymptotic reaction zones

Reaction rate can be locally negative

Concentrations of A and B can be nonmonotonic and exceed initial values

Abstract

We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B <-> C with initially separated reactants. Using it we find that there are three types of asymptotic reaction zones. In particular we show that the reaction rate can be locally negative and concentrations of species A and B can be nonmonotonic functions of the space coordinate x, locally significantly exceeding their initial values.