Using functional analytical and graph theoretical methods, we extend the results of [12] 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.2000 Mathematics Subject Classification: 35F25; 34B15.Our aim is-based on the paper [12]-to handle more general transport processes allowing space dependent velocities and absorption in networks. We model the problem by a system of partial di¤erential equations on a directed graph where the vertices serve as linking points between the edges. We show that the flow is (up to §

We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral properties, the problem of unitary equivalence of typical operators, and their embeddability into C 0 -semigroups. Our results provide information on the applicability of Baire category methods in the theory of Hilbert space operators.

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We prove that any finite simple graph can be covered by three of its odd subgraphs, and we construct an infinite sequence of graphs where an edge-disjoint covering by three odd subgraphs is not possible. c

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