On reaction-subdiffusion equations

TL;DR

This paper explores reaction-subdiffusion equations for a simple A to B conversion, revealing their unusual form due to non-Markovian subdiffusion and highlighting differences from classical reaction-diffusion equations.

Contribution

It derives novel kinetic equations for reaction-subdiffusion processes, showing how reaction parameters influence diffusion and the equations' structure.

Findings

Reaction-subdiffusion equations differ significantly from classical ones.

Reaction parameters affect the diffusion term in the equations.

The equations include history-dependent terms reflecting non-Markovian behavior.

Abstract

To analyze possible generalizations of reaction-diffusion schemes for the case of subdiffusion we discuss a simple monomolecular conversion A --> B. We derive the corresponding kinetic equations for local A and B concentrations. Their form is rather unusual: The parameters of reaction influence the diffusion term in the equation for a component A, a consequence of the nonmarkovian nature of subdiffusion. The equation for a product contains a term which depends on the concentration of A at all previous times. Our discussion shows that reaction-subdiffusion equations may not resemble the corresponding reaction-diffusion ones and are not obtained by a trivial change of the diffusion operator for a subdiffusion one.