Thin layer approximation, boundary conditions and semi-permeable membranes

Adam Bobrowski (University of Heidelberg) #

Think of a reaction-diffusion equation in a region characterised by two linear dimensions, one large the other small, like domains bounded by locally parallel surfaces, such as concentric spheres, coaxial tubes or simply parallel planes. What happens to the differential equation, and its solutions, as `the thickness’ of the domain gets smaller and smaller? Is there a reasonable limit, and what becomes of the boundary conditions accompanying the original equation? What about a similar situation with two thin regions separated by a semipermeable membrane? These questions will be addressed, and to some extent answered, during my talk.