Flows on metric graphs with general boundary conditionsEngel, Klaus-Jochen (Avtor) Kramar Fijavž, Marjeta (Avtor) first order differential operatorstransport equationC$_0$-semigroupsflows on networksnon-compact metric graphsIn this note we study the generation of C$_0$-semigroups by first-order differential operators on L$^p(\mathbb{R}_+, \mathbb{C}^l$) × L$^p$([0, 1], $\mathbb{C}^m$) with general boundary conditions. In many cases we are able to characterize the generation property in terms of the invertibility of a matrix associated to the boundary conditions. The abstract results are used to study the well-posedness of transport equations on non-compact metric graphs.20222022-04-20 11:36:42Članek v reviji136221UDK: 517.98ISSN pri članku: 0022-247XDOI: 10.1016/j.jmaa.2022.126214COBISS_ID: 105351427sl