Stationary spatial structures in reaction-subdiffusion

TL;DR

This paper investigates stationary reactant concentrations in a subdiffusive medium, revealing unique spatial structures and reaction behaviors that differ significantly from classical diffusion models.

Contribution

It introduces a stationary reaction-diffusion framework with nonlinear diffusion for subdiffusive systems, highlighting novel concentration profiles and reaction zone behaviors.

Findings

Existence of accumulation and depletion zones near boundaries

Non-monotonous reaction intensity with source strength

Distinct concentration profiles compared to simple diffusion

Abstract

We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of reactants' concentrations and of reaction zones in a flat subdiffusive medium fed by reactants of both types on its both sides (a subdiffusive gel reactor). The behavior of the concentrations and of the reaction intensity in subdiffusion differs strikingly from those in simple diffusion. The most important differences correspond to the existence of accumulation and depletion zones close to the boundaries and to non-monotonous behavior of the reaction intensity with respect to the strength of the minor source. The implications of these results for other situations are also discussed.