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Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour

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 Łodź University of Technology, Poland

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  • In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.

    Mathematics Subject Classification: Primary: 35B40, 47D03; Secondary: 35L50, 35R02.


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  • Figure 1.  The graph for the problem (30) with the directions of the flows

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