Conservation laws on complex networks

Mauro Garavello, Benedetto Piccoli

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


This paper considers a system described by a conservation law on a general network and deals with solutions to Cauchy problems. The main application is to vehicular traffic, for which we refer to the Lighthill-Whitham-Richards (LWR) model. Assuming to have bounds on the conserved quantity, we are able to prove existence of solutions to Cauchy problems for every initial datum in Lloc1. Moreover Lipschitz continuous dependence of the solution with respect to initial data is discussed.

Original languageEnglish (US)
Pages (from-to)1925-1951
Number of pages27
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number5
StatePublished - 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics


  • Networks
  • Scalar conservation laws
  • Traffic flow
  • Wave-front tracking


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