Using functional analytical and graph theoretical methods, we extend the results of  to more general transport processes in networks allowing space dependent velocities and absorption. We characterize asymptotic periodicity and convergence to an equilibrium by conditions on the underlying directed graph and the (average) velocities.
Combining functional analytical and graph theoretical methods, we investigate flow processes as in the papers  and , but we change the transmission process in the nodes of the network. Instead of conservation of mass, we assume that the velocity of the outgoing flow mass in the vertices is determined by the total incoming flow mass and by the… (More)
We combine functional analytical and graph theoretical methods in order to study flows in networks. We show that these flows can be described by a strongly continuous operator semigroup on a Banach space. Using Perron-Frobenius spectral theory we then prove that this semigroup behaves asymptotically periodic.