Continuous versus discrete description of the transport in a membrane system

The continuous (macroscopic) and the discrete (microscopic) description of the membrane transport are related to each other. Specifically, we construct the Greenʹs functions for a diffusive-convective system with a membrane (which is treated as a partially permeable wall) in three cases: in the first one the Smoluchowski (diffusion) equation (SE) is used, in the second case one applies the birth-death (BDE) equation, and finally, we combine the continuous and discrete description in such a way that in the space outside the wall the SE acts, whereas the passing through the membrane is described in terms of BDE. To obtain the Greenʹs functions in the above-mentioned cases, we introduced a new generalized method of images.