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

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Authors

Banasiak, Jacek
Bloch, Adam

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American Institute of Mathematical Sciences

Abstract

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.

Description

The research was completed while the author was a Doctoral Candidate in the Interdisciplinary Doctoral School at the Lodz University of Technology, Poland.

Keywords

Hyperbolic systems, Networks, Semigroups of operators, Port-Hamiltonians, Saint-Venant system, Kirchhoff's conditions

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Citation

Jacek 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.