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

Jacek Banasiak | Zendy; Adam Błoch | Zendy

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

Author(s) -

Jacek Banasiak,

Adam Błoch

Publication year - 2021

Publication title -

evolution equations and control theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.665

H-Index - 19

eISSN - 2163-2480

pISSN - 2163-2472

DOI - 10.3934/eect.2021046

Subject(s) - semigroup , mathematics , riemann hypothesis , type (biology) , boundary (topology) , relation (database) , boundary value problem , reduction (mathematics) , port (circuit theory) , transmission (telecommunications) , pure mathematics , mathematical analysis , computer science , telecommunications , geometry , geology , engineering , database , electrical engineering , paleontology

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.

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