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Boundary conditions at a thin membrane for normal diffusion, classical subdiffusion, and slow subdiffusion processes
Author(s) -
Kosztołowicz Tadeusz,
Dutkiewicz Aldona
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6539
Subject(s) - diffusion , mathematics , membrane , random walk , anomalous diffusion , boundary (topology) , boundary value problem , statistical physics , space (punctuation) , mathematical analysis , continuous time random walk , physics , chemistry , thermodynamics , innovation diffusion , statistics , computer science , knowledge management , operating system , biochemistry
We consider three different diffusion processes in a system with a thin membrane: normal diffusion, classical subdiffusion, and slow subdiffusion. We conduct the considerations following the rule: If a diffusion equation is derived from a certain theoretical model, boundary conditions at a thin membrane should also be derived from this model with additional assumptions taking into account selective properties of the membrane . To derive diffusion equations and boundary conditions at a thin membrane, we use a particle random walk model in one‐dimensional membrane system in which space and time variables are discrete. Then we move from discrete to continuous variables. We show that the boundary conditions depend on both selective properties of the membrane and a type of diffusion in the system.