ABSTRACT
In a large number of cases a physical system is appropriately described by a system of two (or more) equations associated with phenomena occurring on different spatial scales. Here we consider some cases in which at least one of the equations is parabolic and the coupling between the processes at the two scales may be nonlocal in space and in time. Free boundaries can also be present. After a general discussion we present some specific problem in more detail, pointing out the questions remaining open.
