Existence of solutions to Cauchy problems for a mixed continuum-discrete model for supply chains and networks

C. D'Apice, R. Manzo, B. Piccoli

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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 languageEnglish (US)
Pages (from-to)374-386
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume362
Issue number2
DOIs
StatePublished - Feb 15 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • BV estimates
  • Conservation laws
  • Supply chains

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