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

摘要

Subdiffusion with reaction A + B -> 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 variables, 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 derivative(alpha 1) P(0 (broken vertical bar) ,t) / partial derivative t(alpha 1) = (D-1 / D2) partial derivative(alpha 2) P(0(-), t) / partial derivative 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. Published by AIP Publishing.