A fractal graph model of capillary type systems

The capillary system is modelled by a fractal graph attached to a blood vessel. It is supplied with differential equations obtained from threedimensional model by the dimension-reduction procedure. The geometry and physical parameters of this system are described by a finite number of scaling parameters which allows for system to have self-reproducing solutions, solutions which are determined by theirs values on a certain finite piece of the fractal graph and are continued on the remaining part by using these scaling factors. We describe all self-reproducing solutions and, as a result we obtain a connection between the pressure and the flux at the junction point between the capillary system and blood vessel. This connection gives an artificial boundary condition at the junction in the blood vessel and allows to solve the problem for the flow in the blood vessel without solving it in the capillary system.