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Minimising stop and go waves to optimise traffic flow. (English) Zbl 1058.49011
Summary: 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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