|Abstract:|| In this paper we consider the coupling between two
diffusion-reaction problems, one taking place in a three-dimensional
domain, the other in a one-dimensional subdomain.
This coupled problem is the simplest model of fluid flow in a
three-dimensional porous medium featuring fractures that can be
described by one-dimensional manifolds. In particular this model
can provide the basis for a multiscale analysis of blood flow
through tissues, in which the capillary network is represented as a
porous matrix, while the major blood vessels are described by thin
tubular structures embedded into it: in this case, the model allows
the computation of the 3D and 1D blood pressures respectively in the
tissue and in the vessels.