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Conservation laws on complex networks. (English) Zbl 1181.35144

Summary: 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.

MSC:

35L65 Hyperbolic conservation laws
90B20 Traffic problems in operations research
35L45 Initial value problems for first-order hyperbolic systems
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References:

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