Minimising stop and go waves to optimise traffic flow.

*(English)*Zbl 1058.49011Summary: Motivated by the problem of minimising the “stop and go” phenomenon in traffic flow, we consider a nonstandard problem of calculus of variations. Given a system of hyperbolic conservation laws, we introduce an integral functional where the integrating measure depends on the space derivative of the solution to the conservation law. An existence result for initial and, when present, boundary data that minimise this functional is proved.

##### MSC:

49J45 | Methods involving semicontinuity and convergence; relaxation |

35L65 | Hyperbolic conservation laws |

49J10 | Existence theories for free problems in two or more independent variables |

90B20 | Traffic problems in operations research |

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\textit{R. M. Colombo} and \textit{A. Groli}, Appl. Math. Lett. 17, No. 6, 697--701 (2004; Zbl 1058.49011)

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