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We present the model of a diffusion-absorption process in a system whichconsists of two media separated by a thin partially permeable membrane. Thekind of diffusion as well as the parameters of the process may be different inboth media. Based on a simply model of particle's random walk in a membranesystem we derive the Green's functions, then we find the boundary conditions atthe membrane. One of the boundary conditions are rather complicated and takes arelatively simple form in terms of the Laplace transform. Assuming thatparticles diffuse independently of one another, the obtained boundaryconditions can be used to solve to differential or differential-integralequations describing the processes in multilayered systems for any initialcondition. We consider normal diffusion, subdiffusion and slow subdiffusionprocesses, and we also suggest how superdiffusion could be included in thismodel. The presented method provides the functions in terms of the Laplacetransform and some useful methods of calculation the inverse Laplace transformare shown.

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