Open Access
| Issue |
ESAIM: M2AN
Volume 55, Number 6, November-December 2021
|
|
|---|---|---|
| Page(s) | 2705 - 2723 | |
| DOI | https://doi.org/10.1051/m2an/2021073 | |
| Published online | 17 November 2021 | |
- A. Aggarwal, R.M. Colombo and P. Goatin, Nonlocal systems of conservation laws in several space dimensions. SIAM J. Numer. Anal. 53 (2015) 963–983. [Google Scholar]
- P. Amorim, R.M. Colombo and A. Teixeira, On the numerical integration of scalar nonlocal conservation laws. ESAIM: M2AN 49 (2015) 19–37. [CrossRef] [EDP Sciences] [Google Scholar]
- F. Betancourt, R. Bürger, K.H. Karlsen and E.M. Tory, On nonlocal conservation laws modelling sedimentation. Nonlinearity 24 (2011) 855–885. [CrossRef] [MathSciNet] [Google Scholar]
- S. Blandin and P. Goatin, Well-posedness of a conservation law with non-local flux arising in traffic flow modeling. Numer. Math. 132 (2016) 217–241. [Google Scholar]
- A. Bressan and W. Shen, On traffic flow with nonlocal flux: a relaxation representation. Arch. Rat. Mech. Anal. 237 (2020) 1213–1236. [CrossRef] [Google Scholar]
- A. Bressan and W. Shen, Entropy admissibility of the limit solution for a nonlocal model of traffic flow. Comm. Math. Sci. 19 (2021) 1447–1450. [CrossRef] [Google Scholar]
- F.A. Chiarello and P. Goatin, Non-local multi-class traffic flow models. Netw. Heterog. Media 14 (2019) 371–387. [Google Scholar]
- G.M. Coclite, J.-M. Coron, N. De Nitti, A. Keimer and L. Pflug, A general result on the approximation of local conservation laws by nonlocal conservation laws: the singular limit problem for exponential kernel. Preprint arXiv:2012.13203 (2020). [Google Scholar]
- G.M. Coclite, N. De Nitti, A. Keimer and L. Pflug, Singular limits with vanishing viscosity for nonlocal conservation laws. Nonlinear Anal. Theory Methods App. 211 (2021) 112370. [CrossRef] [Google Scholar]
- R.M. Colombo, M. Garavello and M. Lécureux-Mercier, A class of nonlocal models for pedestrian traffic. Math. Models Methods Appl. Sci. 22 (2012) 1150023. [CrossRef] [MathSciNet] [Google Scholar]
- M. Colombo, G. Crippa and L.V. Spinolo, On the singular local limit for conservation laws with nonlocal fluxes. Arch. Rat. Mech. Anal. 233 (2019) 1131–1167. [CrossRef] [Google Scholar]
- M. Colombo, G. Crippa, E. Marconi and L.V. Spinolo, Local limit of nonlocal traffic models: convergence results and total variation blow-up. Ann. Inst. Henri Poincaré Anal. Non Linéaire 38 (2021) 1653–1666. [CrossRef] [MathSciNet] [Google Scholar]
- G. Crippa and M. Lécureux-Mercier, Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow. NoDEA Nonlinear Differ. Equ. Appl. 20 (2013) 523–537. [CrossRef] [Google Scholar]
- J. Friedrich, O. Kolb and S. Göttlich, A Godunov type scheme for a class of LWR traffic flow models with non-local flux. Netw. Heterog. Media 13 (2018) 531–547. [CrossRef] [MathSciNet] [Google Scholar]
- P. Goatin and S. Scialanga, Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity. Netw. Heterog. Media 11 (2016) 107–121. [Google Scholar]
- A. Keimer and L. Pflug, On approximation of local conservation laws by nonlocal conservation laws. J. Math. Anal. App. 475 (2019) 1927–1955. [CrossRef] [Google Scholar]
- S.N. Kružkov, First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81 (1970) 228–255. [Google Scholar]
- R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge (2002). [Google Scholar]
- S. Osher, Riemann solvers, the entropy condition, and difference. SIAM J. Numer. Anal. 21 (1984) 217–235. [CrossRef] [MathSciNet] [Google Scholar]
- E. Tadmor, Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comput. 43 (1984) 369–381. [Google Scholar]
- E. Tadmor, Chapter 18 – Entropy stable schemes. In: Handbook of Numerical Methods for Hyperbolic Problems, edited by R. Abgrall and C.-W. Shu. Vol. 17 of Handbook of Numerical Analysis . Elsevier (2016) 467–493. [Google Scholar]
- K. Zumbrun, On a nonlocal dispersive equation modeling particle suspensions. Quart. Appl. Math. 57 (1999) 573–600. [CrossRef] [MathSciNet] [Google Scholar]
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