Linear hyperbolic systems on networksKramar Fijavž, Marjeta (Avtor) Mugnolo, Delio (Avtor) Nicaise, Serge (Avtor) hyperbolic systemsoperator semigroupsPDEs on networksinvariance propertiesSaint-Venant systemsecond soundWe study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks, can be reformulated in our rather flexible formalism, which generalizes the classical technique of first-order reduction. We study forward and backward well-posedness; furthermore, we provide necessary and sufficient conditions on both the boundary conditions and the coefficients arising in the first-order reduction for a given subset of the relevant ambient space to be invariant under the flow that governs the system. Several examples are studied.20212021-03-04 15:11:40Članek v reviji125104UDK: 51ISSN pri članku: 1292-8119DOI: 10.1051/cocv/2020091COBISS_ID: 51482883OceCobissID: 513891097sl