A + B → 0 Reaction Under Non-Markovian Subdiffusive Kinetics: Equations and Stationary Solutions

We consider an A + B → 0 reaction in a flat subdiffusive medium in contact with two well mixed reservoirs of particles of both types on the sides. We show that the behaviour of the stationary concentration and reaction intensity profiles in subdiffusion differs strikingly from that observed in simple diffusion. The most marked differences correspond to accumulation peaks and depletion zones in the concentration profile. The height of these peaks as well as the height of the reaction zones exhibit a non- monotonic behaviour with respect to the reactant's concentrations at the boundaries. These characteristics are due to an effectively nonlinear transport under reaction which emerges from the non-Markovian property of the subdiffusion process. (author)