Spectral properties and asymptotic periodicity of flows in networks

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.This paper was written during the authors stay at the Mathematisches Institut der Universität Tübingen. The first author was supported by Virtugrade Baden-Württenberg and the second by the Marie Curie Host Fellowship Spectral theory for evolution equations contract number HPMT-CT-2001-00315. Both authors thank Rainer Nagel for many helpful discussions.