Non-Markovian Random Walks and Non-Linear Reactions: Subdiffusion and Propagating Fronts

TL;DR

This paper develops a reaction-transport model for systems with non-Markovian subdiffusive behavior and non-linear reactions, deriving equations for particle density and analyzing front propagation speeds.

Contribution

It introduces a novel mesoscopic equation for reaction-transport systems with anomalous diffusion and non-linear reactions, including an explicit front speed formula for subdiffusive transport.

Findings

Derived a non-linear evolution equation for particle density

Obtained an explicit expression for front propagation speed in subdiffusion

Applied the model to reaction-transport systems with anomalous diffusion

Abstract

We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of fronts propagation into unstable state of reaction-transport systems with anomalous diffusion. We have found an explicit expression for the speed of propagating front in the case of subdiffusion transport.