JournalsaihpcVol. 26, No. 5pp. 1925–1951

Conservation laws on complex networks

  • Mauro Garavello

    Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale “A. Avogadro”, viale Teresa Michel 11, 15121 Alessandria, Italy
  • Benedetto Piccoli

    I.A.C., C.N.R., Via dei Taurini 19, 00185 Roma, Italy
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Abstract

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 Lloc1L_{\mathrm{loc}}^{1}. Moreover Lipschitz continuous dependence of the solution with respect to initial data is discussed.

Cite this article

Mauro Garavello, Benedetto Piccoli, Conservation laws on complex networks. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, pp. 1925–1951

DOI 10.1016/J.ANIHPC.2009.04.001