Open Access
Issue |
ESAIM: M2AN
Volume 56, Number 3, May-June 2022
|
|
---|---|---|
Page(s) | 1081 - 1114 | |
DOI | https://doi.org/10.1051/m2an/2022030 | |
Published online | 13 May 2022 |
- B. Andreianov, New approaches to describing admissibility of solutions of scalar conservation laws with discontinuous flux. ESAIM: Proc. Surv. 50 (2015) 40–65. [CrossRef] [EDP Sciences] [Google Scholar]
- B. Andreianov and D. Mitrović, Entropy conditions for scalar conservation laws with discontinuous flux revisited. Ann. Inst. Henri Poincaré Anal. Non Linéaire 32 (2015) 1307–1335. [CrossRef] [MathSciNet] [Google Scholar]
- B. Andreianov and A. Sylla, A macroscopic model to reproduce self-organization at bottlenecks. In: International Conference on Finite Volumes for Complex Applications. Springer (2020) 243–254. [Google Scholar]
- B. Andreianov, P. Goatin and N. Seguin, Finite volume schemes for locally constrained conservation laws. Numer. Math. 115 (2010) 609–645. [Google Scholar]
- B. Andreianov, K. Karlsen and N.H. Risebro, A theory of L1-dissipative solvers for scalar conservation laws with discontinuous flux. Arch. Ration. Mech. Anal. 201 (2011) 27–86. [CrossRef] [MathSciNet] [Google Scholar]
- A. Bressan, G. Guerra and W. Shen, Vanishing viscosity solutions for conservation laws with regulated flux. J. Differ. Equ. 266 (2019) 312–351. [CrossRef] [Google Scholar]
- C. Cancès and T. Gallouët, On the time continuity of entropy solutions. J. Evol. Equ. 11 (2011) 43–55. [CrossRef] [MathSciNet] [Google Scholar]
- C. Chalons, M.L. Delle Monache and P. Goatin, A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem. Interfaces Free Boundaries 19 (2018) 553–570. [CrossRef] [Google Scholar]
- R.M. Colombo and P. Goatin, A well posed conservation law with a variable unilateral constraint. J. Differ. Equ. 234 (2007) 654–675. [CrossRef] [Google Scholar]
- R.M. Colombo, M. Mercier and M.D. Rosini, Stability and total variation estimates on general scalar balance laws. Commun. Math. Sci. 7 (2009) 37–65. [CrossRef] [MathSciNet] [Google Scholar]
- M.L. Delle Monache and P. Goatin, Scalar conservation laws with moving constraints arising in traffic flow modeling: An existence result. J. Differ. Equ. 257 (2014) 4015–4029. [CrossRef] [Google Scholar]
- M.L. Delle Monache and P. Goatin, A numerical scheme for moving bottlenecks in traffic flow. Bull. Braz. Math. Soc., New Ser. 47 (2016) 605–617. [CrossRef] [Google Scholar]
- M.L. Delle Monache and P. Goatin, Stability estimates for scalar conservation laws with moving flux constraints. Netw. Heterogen. Media 12 (2017) 245–258. [CrossRef] [Google Scholar]
- M.L. Delle Monache, T. Liard, B. Piccoli, R. Stern and D. Work, Traffic reconstruction using autonomous vehicles. SIAM J. Appl. Math. 79 (2019) 1748–1767. [CrossRef] [MathSciNet] [Google Scholar]
- R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods. Vol . In: Handbook of Numerical Analysis. Vol. VII, North-Holland, Amsterdam (2000). [Google Scholar]
- A. Ferrara, P. Goatin and G. Piacentini, A macroscopic model for platooning in highway traffic. SIAM J. Appl. Math. 80 (2020) 639–656. [CrossRef] [MathSciNet] [Google Scholar]
- M. Garavello, P. Goatin, T. Liard and B. Piccoli, A multiscale model for traffic regulation via autonomous vehicles. J. Differ. Equ. 269 (2020) 6088–6124. [CrossRef] [Google Scholar]
- I. Gasser, C. Lattanzio and A. Maurizi, Vehicular traffic flow dynamics on a bus route. Multiscale Model. Simul. 11 (2013) 925–942. [CrossRef] [MathSciNet] [Google Scholar]
- H. Holden and N.H. Risebro, Front Tracking for Hyperbolic Conservation Laws. In: Applied Mathematical Sciences. Vol. 152, Springer-Verlag, New York (2002). [CrossRef] [Google Scholar]
- K.H. Karlsen and J.D. Towers, Convergence of the lax-friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. Chin. Ann. Math. 25 (2004) 287–318. [CrossRef] [Google Scholar]
- S.N. Kruzhkov, First order quasilinear equations with several independent variables. Math. USSR-Sbornik 81 (1970) 228–255. [Google Scholar]
- N. Laurent-Brouty, G. Costeseque and P. Goatin, A macroscopic traffic flow model accounting for bounded acceleration. SIAM J. Appl. Math. 81 (2021) 173–189. [CrossRef] [MathSciNet] [Google Scholar]
- A. Sylla, Heterogeneity in scalar conservation laws: Approximation and applications, Ph.D. thesis, University of Tours (2021). [Google Scholar]
- A. Sylla, Influence of a slow moving vehicle on traffic: Well-posedness and approximation for a mildly nonlocal model. Netw. Heterogen. Media 16 (2021) 221–256. [CrossRef] [Google Scholar]
- J.D. Towers, Convergence via OSLC of the Godunov scheme for a scalar conservation law with time and space flux discontinuities. Numer. Math. 139 (2018) 939–969. [CrossRef] [MathSciNet] [Google Scholar]
- J.D. Towers, An existence result for conservation laws having BV spatial flux heterogeneities-without concavity. J. Differ. Equ. 269 (2020) 5754–5764. [CrossRef] [Google Scholar]
- A.I. Vol’pert, The spaces BV and quasilinear equations. Mat. Sb. 115 (1967) 255–302. [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.