A proof of Kirchhoff’s first law for hyperbolic conservation laws on networks

Bayen AM, Keimer A, Müller N (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Networks and Heterogeneous Media

Book Volume: 18

Pages Range: 1799-1819

Journal Issue: 4

DOI: 10.3934/NHM.2023078

Abstract

In dynamical systems on networks, Kirchhoff’s first law describes the local conservation of a quantity across edges. Predominantly, Kirchhoff’s first law has been conceived as a phenomenological law of continuum physics. We establish its algebraic form as a property that is inherited from fundamental axioms of a network’s geometry, instead of a law observed in physical nature. To this end, we extend calculus to networks, modeled as abstract metric spaces, and derive Kirchhoff’s first law for hyperbolic conservation laws. In particular, our results show that hyperbolic conservation laws on networks can be stated without explicit Kirchhoff-type boundary conditions.

Authors with CRIS profile

Alexander Keimer Lehrstuhl für Analysis

Involved external institutions

Max Planck Institute for Software Systems (MPI-SWS) DE Germany (DE)

How to cite

APA:

Bayen, A.M., Keimer, A., & Müller, N. (2023). A proof of Kirchhoff’s first law for hyperbolic conservation laws on networks. Networks and Heterogeneous Media, 18(4), 1799-1819. https://doi.org/10.3934/NHM.2023078

MLA:

Bayen, Alexandre M., Alexander Keimer, and Nils Müller. "A proof of Kirchhoff’s first law for hyperbolic conservation laws on networks." Networks and Heterogeneous Media 18.4 (2023): 1799-1819.

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