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Pré-Publication, Document De Travail Année : 2018

Well-posedness for scalar conservation laws with moving flux constraints

Thibault Liard
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  • IdRef : 198527594
Benedetto Piccoli
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  • PersonId : 931675

Résumé

We consider a strongly coupled ODE-PDE system representing moving bottlenecks immersed in vehicular traffic. The PDE consists of a scalar conservation law modeling the traffic flow evolution and the ODE models the trajectory of a slow moving vehicle. The moving bottleneck influences the bulk traffic flow via a point flux constraint, which is given by an inequality on the flux at the slow vehicle position. We prove uniqueness and continuous dependence of solutions with respect to initial data of bounded variation. The proof is based on a new backward in time method established to capture the values of the norm of generalized tangent vectors at every time.
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Dates et versions

hal-01684506 , version 1 (15-01-2018)

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Thibault Liard, Benedetto Piccoli. Well-posedness for scalar conservation laws with moving flux constraints. 2018. ⟨hal-01684506⟩
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