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Semigroup approach to diffusion and transport problems on networks. (English) Zbl 1358.90018

Summary: Models describing transport and diffusion processes occurring along the edges of a graph and interlinked by its vertices have been recently receiving a considerable attention. In this paper we generalize such models and consider a network of transport or diffusion operators defined on one dimensional domains and connected through boundary conditions linking the end-points of these domains in an arbitrary way (not necessarily in the way the edges of a graph are connected). We prove the existence of \(C_0\)-semigroups solving such problems and provide conditions fully characterizing when they are positive.

MSC:

90B10 Deterministic network models in operations research
20M99 Semigroups
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