From the solutions of diffusion equation to the solutions of subdiffusive one

Details From the solutions of diffusion equation to the solutions of subdiffusive one From the solutions of diffusion equation to the solutions of subdiffusive one

2004-04-14

arxiv.org/abs/cond-mat/0404342v2

Physics

Condensed Matter

Statistical Mechanics

11 pages, 2 figures

Scientific paper

10.1088/0305-4470/37/45/005

Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of fluxes and concentrations. The method is particularly useful to calculate the concentration profiles in a multi-part system where different kind of transport occurs in each part of it. As an example, we find the solutions of subdiffusive equation for the system composed from two parts with normal diffusion and subdiffusion, respectively.

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