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2019 | 73 | 2 |
Tytuł artykułu

Systems of conservation laws with discontinuous fluxes and applications to traffic

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study \(2\times 2\) systems of conservation laws with discontinuous fluxes arising in vehicular traffic modeling. The main goal is to introduce an appropriate notion of solution. To this aim we consider physically reasonable microscopic follow-the-leader models. Macroscopic Riemann solvers are then obtained as many particle limits. This approach leads us to develop six models. We propose a unified way to describe such models, which highlights their common property of maximizing the density flow across the interface under appropriate physical restrictions depending on the case at hand.
Rocznik
Tom
73
Numer
2
Opis fizyczny
Daty
wydano
2019
online
2020-01-16
Twórcy
Bibliografia
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  • Adimurthi, Dutta, R., Gowda, G. D. V., Jaffre, J., Monotone (A,B) entropy stable numerical scheme for scalar conservation laws with discontinuous flux, ESAIM Math. Model. Numer. Anal. 48 (6) (2014), 1725–1755.
  • Adimurthi, Mishra, S., Gowda, G. D. V., Optimal entropy solutions for conservation laws with discontinuous flux-functions, J. Hyperbolic Differ. Equ. 2 (4) (2005), 783–837.
  • Adimurthi, Mishra, S., Gowda, G. D. V., Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes, Netw. Heterog. Media 2 (1) (2007), 127–157.
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  • Andreianov, B., New approaches to describing admissibility of solutions of scalar conservation laws with discontinuous flux, in: CANUM 2014 – 42e Congres National d’Analyse Numerique, ESAIM Proc. Surveys 50 EDP Sci., Les Ulis, 2015, 40–65.
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  • Andreianov, B., Cances, C., On interface transmission conditions for conservation laws with discontinuous flux of general shape, J. Hyperbolic Differ. Equ. 12 (2) (2015), 343–384.
  • Andreianov, B., Donadello, C., Rosini, M. D., A second-order model for vehicular traffics with local point constraints on the flow, Math. Models Methods Appl. Sci. 26 (4) (2016), 751–802.
  • Andreianov, B., Karlsen, K. H., Risebro, N. H., A theory of \(L^1\)-dissipative solvers for scalar conservation laws with discontinuous flux, Arch. Ration. Mech. Anal. 201 (1) (2011), 27–86.
  • Andreianov, B., Mitrovic, D., Entropy conditions for scalar conservation laws with discontinuous flux revisited, Ann. Inst. H. Poincare Anal. Non Lineaire 32 (6) (2015), 1307–1335.
  • Andreianov, B., Rosini, M. D., Microscopic selection of solutions to scalar conservation laws with discontinuous flux in the context of vehicular traffic, submitted, 2019.
  • Aw, A., Rascle, M., Resurrection of “second order” models of traffic flow, SIAM J. Appl. Math. 60 (3) (2000), 916–938.
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  • Karlsen, K. H., Risebro, N. H., Towers, J. D., \(L^1\) stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients, Skr. K. Nor. Vidensk. Selsk. 3 (2003), 49 pp.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2019_73_2_135-173
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