Reaction-subdiffusion equations for the A-B reaction

Abstract

We consider a linear reversible isomerization reaction A B under subdiffusion described by continuous time random walks (CTRW). The reactants transformations take place independently on the motion and are described by constant rates. We show that the form of the ensuing system of mesoscopic reaction-subdiffusion equations is unusual: the equation for time derivative of say A(x,t) contains the terms depending not only on DeltaA, but also on DeltaB. This mirrors the fact that in subdiffusion the flux of particles at time t is defined by the distributions of the particles concentrations at all previous times. Since the particles which jump as A at time t could previously be both A or B, this flux depends on both A and B concentrations.