Conservation laws on complex networks

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