Asymptotic scaling in a model class of anomalous reaction-diffusion equations

TL;DR

This paper investigates the long-term scaling behavior of a class of anomalous reaction-diffusion equations, providing both numerical evidence and an analytical framework to understand their asymptotic symmetry properties.

Contribution

It introduces a general analytical framework to explain the asymptotic scaling and symmetry properties observed in anomalous reaction-diffusion equations.

Findings

Solutions exhibit well-defined scaling properties at large times

The framework explains the observed asymptotic symmetry behaviors

Numerical experiments support the analytical results

Abstract

We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large $t$, well defined scaling properties. We suggest a general framework to analyze asymptotic symmetry properties; this provides an analytical explanation of the observed asymptotic scaling properties for the considered ARD equations.