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Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 1):021111. Epub 2008 Feb 11.

Anomalous subdiffusion with multispecies linear reaction dynamics.

Author information

1
Department of Applied Mathematics, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, Australia.

Abstract

We have introduced a set of coupled fractional reaction-diffusion equations to model a multispecies system undergoing anomalous subdiffusion with linear reaction dynamics. The model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics. The effect of reactions is manifest in reaction modified spatiotemporal diffusion operators as well as in additive mean field reaction terms. One consequence of the nonseparability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species. The general solution is derived for the multispecies system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail. We have carried out Monte Carlo simulations corresponding to these special cases and we find excellent agreement with theory.

PMID:
18351991
DOI:
10.1103/PhysRevE.77.021111

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