Banasiak, JacekBloch, Adam2022-06-082022-06-082022Jacek Banasiak, Adam Błoch. Telegraph systems on networks and port-Hamiltonians. I. Boundary conditions and well-posedness. Evolution Equations and Control Theory, vol. 11, no. 4, pp. 1331-1355. doi: 10.3934/eect.2021046.2163-2480 (online)10.3934/eect.2021046https://repository.up.ac.za/handle/2263/85747The research was completed while the author was a Doctoral Candidate in the Interdisciplinary Doctoral School at the Lodz University of Technology, Poland.The paper is concerned with a system of linear hyperbolic differential equations on a network coupled through general transmission conditions of Kirchhoff's-type at the nodes. We discuss the reduction of such a problem to a system of 1-dimensional hyperbolic problems for the associated Riemann invariants and provide a semigroup-theoretic proof of its well-posedness. A number of examples showing the relation of our results with recent research is also provided.enAmerican Institute of Mathematical SciencesHyperbolic systemsNetworksSemigroups of operatorsPort-HamiltoniansSaint-Venant systemKirchhoff's conditionsPreprint Article