  We present the model of a diffusion-absorption process in a system which
consists of two media separated by a thin partially permeable membrane. The
kind of diffusion as well as the parameters of the process may be different in
both media. Based on a simply model of particle's random walk in a membrane
system we derive the Green's functions, then we find the boundary conditions at
the membrane. One of the boundary conditions are rather complicated and takes a
relatively simple form in terms of the Laplace transform. Assuming that
particles diffuse independently of one another, the obtained boundary
conditions can be used to solve to differential or differential-integral
equations describing the processes in multilayered systems for any initial
condition. We consider normal diffusion, subdiffusion and slow subdiffusion
processes, and we also suggest how superdiffusion could be included in this
model. The presented method provides the functions in terms of the Laplace
transform and some useful methods of calculation the inverse Laplace transform
are shown.
