Open AccessTelegraph systems on networks and port-Hamiltonians. I. Boundary conditions and well-posedness
Author(s) -
Jacek Banasiak,
Adam Błoch
Publication year - 2022
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.