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

Banasiak, Jacek; Bloch, Adam

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

Banasiak, Jacek; Bloch, Adam

URI: https://repository.up.ac.za/handle/2263/85747

Date: 2022

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.

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