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Scalar conservation laws with moving constraints arising in traffic flow modeling: an existence result

Maria Laura Delle Monache 1 Paola Goatin 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : We consider a strongly coupled PDE-ODE system that describes the influence of a slow and large vehicle on road traffic. The model consists of a scalar conservation law accounting for the main traffic evolution, while the trajectory of the slower vehicle is given by an ODE depending on the downstream traffic density. The moving constraint is expressed by an inequality on the flux, which models the bottleneck created in the road by the presence of the slower vehicle. We prove the existence of solutions to the Cauchy problem for initial data of bounded variation.
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Submitted on : Thursday, April 10, 2014 - 2:18:47 PM
Last modification on : Monday, October 12, 2020 - 2:28:04 PM
Long-term archiving on: : Thursday, July 10, 2014 - 12:15:50 PM

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Maria Laura Delle Monache, Paola Goatin. Scalar conservation laws with moving constraints arising in traffic flow modeling: an existence result. Journal of Differential Equations, Elsevier, 2014, 257, pp.4015-4029. ⟨hal-00976855⟩

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