## Abstract

We consider a continuum-discrete model for supply chains based on partial differential equations. The state space is formed by a graph: The load dynamics obeys to a continuous evolution on each arc, while at nodes the good density is conserved, while the processing rate is adjusted. To uniquely determine the dynamics at nodes, the through flux is maximized, with the minimal possible processing rate change. Existence of solutions to Cauchy problems is proven. The latter is achieved deriving estimates on the total variation of the density flux, density and processing rate along a wave-front tracking approximate solution. Then the extension to supply networks is showed.

Original language | English (US) |
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Pages (from-to) | 374-386 |

Number of pages | 13 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 362 |

Issue number | 2 |

DOIs | |

State | Published - Feb 15 2010 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

## Keywords

- BV estimates
- Conservation laws
- Supply chains