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Telegraph systems on networks and port-Hamiltonians. I. Boundary conditions and well-posedness

J. B. acknowledges partial support from the National Science Centre of Poland Grant 2017/25/B/ST1/00051 and the National Research Foundation of South Africa Grant 82770. The research was completed while A. B. was a doctoral candidate in the Interdisciplinary Doctoral School at Łódź University of Technology, Poland

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  • 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.

    Mathematics Subject Classification: Primary: 35R02; Secondary: 47D03, 35L40.

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  • Figure 1.  Starlike network of channels

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