Free Access
Issue
ESAIM: M2AN
Volume 53, Number 1, January–February 2019
Page(s) 1 - 34
DOI https://doi.org/10.1051/m2an/2019002
Published online 14 March 2019
  1. B. Andreianov, G.M. Coclite and C. Donadello, Well-posedness for vanishing viscosity solutions of scalar conservation laws on a network. Discrete Contin. Dyn. Syst. A 37 (2017) 5913–5942. [CrossRef] [Google Scholar]
  2. B. Andreianov, C. Donadello, U. Razafison and M.D. Rosini, Riemann problems with non–local point constraints and capacity drop. Math. Biosci. Eng. 12 (2015) 259–278. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  3. B. Andreianov, C. Donadello, U. Razafison and M.D. Rosini, Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks. ESAIM: M2AN 50 (2016) 1269–1287. [CrossRef] [EDP Sciences] [Google Scholar]
  4. B. Andreianov, C. Donadello, U. Razafison and M.D. Rosini, Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux. J. Math. Pures App. 116 (2018) 309–346. [CrossRef] [Google Scholar]
  5. B. Andreianov, C. Donadello and M.D. Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop. Math. Models Methods Appl. Sci. 24 (2014) 2685–2722. [Google Scholar]
  6. B. Andreianov, P. Goatin and N. Seguin, Finite volume schemes for locally constrained conservation laws. Numer. Math. 115 (2010) 609–645. [Google Scholar]
  7. C. Bardos, A.Y. Leroux and J.C. Nedelec, First order quasilinear equations with boundary conditions. Commun. Partial Differ. Equ. 4 (1979) 1017–1034. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Bressan, S. Čanić, M. Garavello, M. Herty and B. Piccoli, Flows on networks: recent results and perspectives. EMS Surv. Math. Sci. 1 (2014) 47–111. [CrossRef] [Google Scholar]
  9. C. Cancès and N. Seguin, Error estimate for Godunov approximation of locally constrained conservation laws. SIAM J. Numer. Anal. 50 (2012) 3036–3060. [Google Scholar]
  10. C. Chalons, Numerical approximation of a macroscopic model of pedestrian flows. SIAM J. Sci. Comput. 29 (2007) 539–555. [Google Scholar]
  11. C. Chalons, P. Goatin and N. Seguin, General constrained conservation laws. Application to pedestrian flow modeling.. Networks Heterogen. Media 8 (2013) 433–463. [CrossRef] [MathSciNet] [Google Scholar]
  12. G.M. Coclite, M. Garavello and B. Piccoli, Traffic flow on a road network. SIAM J. Math. Anal. 36 (2005) 1862–1886. [CrossRef] [Google Scholar]
  13. R. Colombo and P. Goatin, A well posed conservation law with a variable unilateral constraint. J. Differ. Equ. 234 (2007) 654–675. [Google Scholar]
  14. R.M. Colombo, P. Goatin and M.D. Rosini, A macroscopic model for pedestrian flows in panic situations. In: Current Advances in Nonlinear Analysis and Related Topics. GAKUTO Internat. Ser. Math. Sci. Appl. Gakkōtosho, Tokyo 32 (2010) 255–272. [Google Scholar]
  15. R.M. Colombo, P. Goatin and M.D. Rosini, On the modelling and management of traffic. ESAIM: M2AN 45 (2011) 853–872. [CrossRef] [EDP Sciences] [Google Scholar]
  16. R.M. Colombo and M.D. Rosini, Pedestrian flows and non-classical shocks. Math. Methods Appl. Sci. 28 (2005) 1553–1567. [Google Scholar]
  17. R.M. Colombo and M.D. Rosini, Existence of nonclassical solutions in a pedestrian flow model. Nonlinear Anal.: Real World App. 10 (2009) 2716–2728. [CrossRef] [Google Scholar]
  18. C. D’Apice, R. Manzo and B. Piccoli, Packet flow on telecommunication networks. SIAM J. Math. Anal. 38 (2006) 717–740. [CrossRef] [Google Scholar]
  19. M. Garavello, K. Han and B. Piccoli, Models for vehicular traffic on networks. Conservation laws models. AIMS Series on Applied Mathematics. American Institute of Mathematical Sciences (AIMS), Springfield, MO 9 (2016). [Google Scholar]
  20. M. Garavello and B. Piccoli, Traffic flow on networks. Conservation laws models. AIMS Series on Applied Mathematics. American Institute of Mathematical Sciences (AIMS), Springfield, MO 1 (2006). [Google Scholar]
  21. M. Garavello and B. Piccoli, Conservation laws on complex networks. Ann. Inst. Henri Poincaré (C) Non Lin. Anal. 26 (2009) 1925–1951. [CrossRef] [Google Scholar]
  22. B. Haut, G. Bastin and Y. Chitour, A macroscopic traffic model for road networks with a representation of the capacity drop phenomenon at the junctions. In Vol. 226 of Proceedings 16th IFAC World Congress, Prague, Czech Republic (2005) Tu–M01–TP/3. [Google Scholar]
  23. S.N. Kruzhkov, First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81 (1970) 228–255. [Google Scholar]
  24. M.J. Lighthill and G.B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London. Ser. A. 229 (1955) 317–345. [Google Scholar]
  25. E.Y. Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws. J. Hyperbolic Differ. Equ. 4 (2007) 729–770. [CrossRef] [MathSciNet] [Google Scholar]
  26. S.F. Pellegrino, On the implementation of a finite volumes scheme with monotone transmission conditions for scalar conservation laws on a star-shaped network. Preprint arXiv:1902.02395 (2019). [Google Scholar]
  27. P.I. Richards, Shock waves on the highway. Oper. Res. 4 (1956) 42–51. [Google Scholar]
  28. M.D. Rosini, Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications. Springer, Heidelberg (2013). [CrossRef] [Google Scholar]
  29. A. Vasseur, Strong traces for solutions of multidimensional scalar conservation laws. Arch. Ration. Mech. Anal. 160 (2001) 181–193. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you