We are interested in physical phenomena where the transportation on an arc of a network is governed by a hyperbolic (system of) conservation or balance laws. These kind of transportation problems on networks have many different applications as for example gas flow in pipes, open water channels, traffic flow or supply chain management. In all the previous cases the dynamics on each arc has to be coupled at intersections to dynamics on adjacent arcs through coupling conditions. We present an overview recent developments of these conditions from a theoretical and numerical point of view.
We emphasize difference between the different areas of applications and their implications to the analysis of the conditions and their relation to nonlinear boundary conditions.