Well-posedness of flows in networks with output

In this note, the transport processes in networks with space dependent velocities on edges and output in a node was discussed by combining functional analytical and graph theoretical methods. This problem was converted into the terminology of operator semigroups and an abstract Cauchy problem was obtained on a suitable Banach space. The well-posedness of the system was given by showing the system operator generates a c₀ semigroups.