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-loc(1). Moreover Lipschitz continuous dependence of the solution with respect to initial data is discussed.
Garavello, M., Piccoli, B. (2009). Conservation laws on complex networks. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 26(5), 1925-1951 [10.1016/j.anihpc.2009.04.001].
Conservation laws on complex networks
GARAVELLO, MAURO;
2009
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-loc(1). Moreover Lipschitz continuous dependence of the solution with respect to initial data is discussed.
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