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Mesoscopic modeling of stochastic reaction-diffusion kinetics in the subdiffusive regime. (English) Zbl 1381.35086

Summary: Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model of subdiffusion into an accurate and consistent reaction-subdiffusion computational framework. Two different possible models of chemical reaction are revealed and some basic dynamic properties are derived. In certain cases those mesoscopic models have a direct interpretation at the macroscopic level as fractional partial differential equations in a bounded time interval. Through analysis and numerical experiments we estimate the macroscopic effects of reactions under subdiffusive mixing. The models display properties also observed in experiments: for a short time interval the behavior of the diffusion and the reaction is ordinary, in an intermediate interval the behavior is anomalous, and at long times the behavior is ordinary again.

MSC:

35K57 Reaction-diffusion equations
35R11 Fractional partial differential equations
60J60 Diffusion processes
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C37 Cell biology
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
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