Riemann problems with non--local point constraints and capacity drop

Abstract : In the present note we discuss in details the Riemann problem for a one--dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the problem, namely in the case, relevant for numerical applications, of a discretized exit capacity. We devote particular attention to the case in which the constraint is given by a non--local operator depending on the solution itself. We provide several explicit examples. We also give the detailed proof of some results announced in the paper [Andreainov, Donadello, Rosini, "Crowd dynamics and conservation laws with non--local point constraints and capacity drop", which is devoted to existence and stability for a more general class of Cauchy problems subject to Lipschitz continuous non--local point constraints.
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Communication dans un congrès
A.S. Ackleh, R.M. Colombo, S.C. Hille and A. Muntean. Modeling with Measures, Aug 2013, Leiden, Netherlands. American Institute of Mathematical Sciences, Mathematical Biosciences and Engineering (MBE), 12 (2), pp. 259-278, 2015, "MODELING WITH MEASURES". 〈10.3934/mbe.2015.12.259〉
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https://hal.archives-ouvertes.fr/hal-00959974
Contributeur : Carlotta Donadello <>
Soumis le : lundi 17 mars 2014 - 13:46:44
Dernière modification le : vendredi 6 juillet 2018 - 15:18:04

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Boris Andreianov, Carlotta Donadello, Ulrich Razafison, Massimiliano Rosini. Riemann problems with non--local point constraints and capacity drop. A.S. Ackleh, R.M. Colombo, S.C. Hille and A. Muntean. Modeling with Measures, Aug 2013, Leiden, Netherlands. American Institute of Mathematical Sciences, Mathematical Biosciences and Engineering (MBE), 12 (2), pp. 259-278, 2015, "MODELING WITH MEASURES". 〈10.3934/mbe.2015.12.259〉. 〈hal-00959974〉

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