Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2211.13730 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910318037303296 |
|---|---|
| author | Bayen, Alexandre M. Keimer, Alexander Müller, Nils |
| author_facet | Bayen, Alexandre M. Keimer, Alexander Müller, Nils |
| contents | Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on networks may capture shared concepts, and provide a setting for deriving abstract properties. To this end, we develop a calculus for networks modeled as abstract metric spaces and derive an analog of Kirchhoff's first law for hyperbolic conservation laws. In dynamical systems on networks, Kirchhoff's first law connects the study of abstract global objects, and that of a computationally-beneficial edgewise-Euclidean perspective by stating its equivalence. In particular, our results show that hyperbolic conservation laws on networks can be stated without explicit Kirchhoff-type boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_13730 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Proof of Kirchhoff's First Law for Hyperbolic Conservation Laws on Networks Bayen, Alexandre M. Keimer, Alexander Müller, Nils Analysis of PDEs Metric Geometry 35R02, 35C99 (Primary) 35L65, 00A71 (Secondary) Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on networks may capture shared concepts, and provide a setting for deriving abstract properties. To this end, we develop a calculus for networks modeled as abstract metric spaces and derive an analog of Kirchhoff's first law for hyperbolic conservation laws. In dynamical systems on networks, Kirchhoff's first law connects the study of abstract global objects, and that of a computationally-beneficial edgewise-Euclidean perspective by stating its equivalence. In particular, our results show that hyperbolic conservation laws on networks can be stated without explicit Kirchhoff-type boundary conditions. |
| title | A Proof of Kirchhoff's First Law for Hyperbolic Conservation Laws on Networks |
| topic | Analysis of PDEs Metric Geometry 35R02, 35C99 (Primary) 35L65, 00A71 (Secondary) |
| url | https://arxiv.org/abs/2211.13730 |