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

TL;DR

This paper studies linear hyperbolic systems on networks with Kirchhoff boundary conditions, demonstrating well-posedness through semigroup theory and connecting results to recent research in the field.

Contribution

It introduces a reduction to Riemann invariants and provides a semigroup approach to establish well-posedness for networked hyperbolic systems.

Findings

Reduction to Riemann invariants simplifies analysis.

Semigroup theory confirms well-posedness.

Examples link results to recent research.

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.