Existence of solutions for scalar conservation laws with moving flux constraints

Abstract : We consider a coupled PDE-ODE model representing a slow moving vehicle immersed in vehicular traffic. The PDE consists of a scalar conservation law modeling the evolution of vehicular traffic and the trajectory of a slow moving vehicle is given by an ODE depending on the downstream traffic density. The slow moving vehicle may be regarded as a moving bottleneck influencing the bulk traffic flow via a moving flux pointwise constraint. We prove existence of solutions with respect to initial data of bounded variation. Approximate solutions are constructed via the wave-front tracking method and their limit are solutions of the Cauchy problem PDE-ODE.
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https://hal.archives-ouvertes.fr/hal-02149946
Contributor : Thibault Liard <>
Submitted on : Thursday, June 6, 2019 - 6:14:45 PM
Last modification on : Saturday, June 8, 2019 - 1:24:31 AM

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Thibault Liard, Benedetto Piccoli. Existence of solutions for scalar conservation laws with moving flux constraints. 2019. ⟨hal-02149946⟩

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