Subdiffusion--absorption process in a system consisting of two different media

Abstract

Subdiffusion with reaction $A+B\to B$ is considered in a system which consists of two homogeneous media joined together; the $A$ particles are mobile whereas $B$ are static. Subdiffusion and reaction parameters, which are assumed to be independent of time and space variable, can be different in both media. Particles $A$ move freely across the border between the media. In each part of the system the process is described by the subdiffusion--reaction equations with fractional time derivative. By means of the method presented in this paper we derive both the fundamental solutions (the Green's functions) $P(x,t)$ to the subdiffusion--reaction equations and the boundary conditions at the border between the media. One of the conditions demands the continuity of a flux and the other one contains the Riemann--Liouville fractional time derivatives ${\partial }^{{\alpha }_1}P(0^{+},t)/\partial t^{{\alpha }_1}=(D_1/D_2){\partial }^{{\alpha }_2}P(0^{-},t)/\partial t^{{\alpha }_2}$, where the subdiffusion parameters ${\alpha }_1$, $D_1$ and ${\alpha }_2$, $D_2$ are defined in the regions $x<0$ and $x>0$, respectively.

7 pages, 6 figures

References in corpus (5)

• Reaction Front in an A+B -> C Reaction-Subdiffusion Process
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Cited by in corpus (1)

• Model of anomalous diffusion--absorption process in a system consisting of two different media separated by a thin membrane