Minimising stop and go waves to optimise traffic flow

Abstract 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.

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