title: Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.
abstract: We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.
authors.affiliation: Department of Applied Mathematics, School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia. B.Henry@unsw.edu.au
authors.forename: B I
authors.initials: BI
authors.lastname: Henry
authors.forename: T A M
authors.initials: TA
authors.lastname: Langlands
authors.forename: S L
authors.initials: SL
authors.lastname: Wearne