EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 57 / No 6 (November-December 2023) ESAIM: M2AN, 57 6 (2023) 3439-3481 References
Open Access
Issue
ESAIM: M2AN
Volume 57, Number 6, November-December 2023
Page(s) 3439 - 3481
DOI https://doi.org/10.1051/m2an/2023080
Published online 29 November 2023
  1. E. Abreu Imecc Unicamp Brazil, R. De la cruz Guerrero, J. Juajibioy and W. Lambert, Lagrangian-eulerian approach for nonlocal conservation laws. J. Dyn Differ. Equ. (2022) 1–47. [Google Scholar]
  2. Adimurthi, K. Sudarshan Kumar and G.D. Veerappa Gowda, Second order scheme for scalar conservation laws with discontinuous flux. Appl. Numer. Math. 80 (2014) 46–64. [CrossRef] [MathSciNet] [Google Scholar]
  3. 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]
  4. A. Aggarwal, H. Holden and G. Vaidya, On the accuracy of the finite volume approximations to nonlocal conservation laws. Preprint arXiv:2306.00142 (2023). [Google Scholar]
  5. D. Amadori, S.-Y. Ha and J. Park, On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation. J. Differ. Equ. 262 (2017) 978–1022. [CrossRef] [Google Scholar]
  6. P. Amorim, On a nonlocal hyperbolic conservation law arising from a gradient constraint problem. Bull. Braz. Math. Soc. New Ser. 43 (2012) 599–614. [CrossRef] [Google Scholar]
  7. P. Amorim, R.M. Colombo and A. Teixeira, On the numerical integration of scalar nonlocal conservation laws. ESAIM Math. Model. Numer. Anal. 49 (2015) 19–37. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  8. D. Armbruster, D.E. Marthaler, C. Ringhofer, K. Kempf and T.-C. Jo, A continuum model for a re-entrant factory. Oper. Res. 54 (2006) 933–950. [CrossRef] [Google Scholar]
  9. A. Bayen, J.-M. Coron, N. De Nitti, A. Keimer and L. Pflug, Boundary controllability and asymptotic stabilization of a nonlocal traffic flow model. Vietnam J. Math. 49 (2021) 957–985. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Berthelin and P. Goatin, Regularity results for the solutions of a non-local model of traffic flow. Discrete Contin. Dyn. Syst. 39 (2019) 3197–3213. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Berthon, Why the MUSCL-Hancock scheme is L1-stable. Numer. Math. 104 (2006) 27–46. [CrossRef] [MathSciNet] [Google Scholar]
  12. C. Berthon and V. Desveaux, An entropy preserving MOOD scheme for the Euler equations. Int. J. Finite 11 (2014) 1–39. [Google Scholar]
  13. 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]
  14. 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]
  15. A. Bressan and W. Shen, On traffic flow with nonlocal flux: a relaxation representation. Arch. Ration. Mech. Anal. 237 (2020) 1213–1236. [CrossRef] [MathSciNet] [Google Scholar]
  16. A. Bressan and W. Shen, Entropy admissibility of the limit solution for a nonlocal model of traffic flow. Commun. Math. Sci. 19 (2021) 1447–1450. [CrossRef] [MathSciNet] [Google Scholar]
  17. R. Bürger, P. Goatin, D. Inzunza and L.M. Villada, A non-local pedestrian flow model accounting for anisotropic interactions and domain boundaries. Math. Biosci. Eng. 17 (2020) 5883–5906. [MathSciNet] [Google Scholar]
  18. R. Bürger, H.D. Contreras and L.M. Villada, A hilliges-weidlich-type scheme for a one-dimensional scalar conservation law with nonlocal flux. Netw. Heterog. Media 18 (2023) 664–693. [CrossRef] [MathSciNet] [Google Scholar]
  19. C. Chalons, P. Goatin and L.M. Villada, High-order numerical schemes for one-dimensional nonlocal conservation laws. SIAM J. Sci. Comput. 40 (2018) A288–A305. [CrossRef] [Google Scholar]
  20. F.A. Chiarello and P. Goatin, Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel. ESAIM Math. Model. Numer. Anal. 52 (2018) 163–180. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  21. F.A. Chiarello and P. Goatin, Non-local multi-class traffic flow models. Netw. Heterog. Media 14 (2019) 371–387. [Google Scholar]
  22. F.A. Chiarello and G.M. Coclite, Nonlocal scalar conservation laws with discontinuous flux. Netw. Heterog. Media 18 (2023) 380–398. [Google Scholar]
  23. F.A. Chiarello and A. Tosin, Macroscopic limits of non-local kinetic descriptions of vehicular traffic. Kinet. Relat. Models 16 (2023) 540–564. [CrossRef] [MathSciNet] [Google Scholar]
  24. F.A. Chiarello, P. Goatin and E. Rossi, Stability estimates for non-local scalar conservation laws. Nonlinear Anal. Real World Appl. 45 (2019) 668–687. [Google Scholar]
  25. F.A. Chiarello, P. Goatin and L.M. Villada, Lagrangian-antidiffusive remap schemes for non-local multi-class traffic flow models. Comput. Appl. Math. 39 (2020) 22. [CrossRef] [Google Scholar]
  26. F.A. Chiarello, J. Friedrich, P. Goatin, S. Göttlich and O. Kolb, A non-local traffic flow model for 1-to-1 junctions. Eur. J. Appl. Math. 31 (2020) 1029–1049. [CrossRef] [Google Scholar]
  27. F.A. Chiarello, H.D. Contreras and L.M. Villada, Nonlocal reaction traffic flow model with on-off ramps. Netw. Heterog. Media 17 (2022) 203–226. [CrossRef] [MathSciNet] [Google Scholar]
  28. I. Ciotir, R. Fayad, N. Forcadel and A. Tonnoir, A non-local macroscopic model for traffic flow. ESAIM Math. Model. Numer. Anal. 55 (2021) 689–711. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  29. G.M. Coclite, J.-M. Coron, N.D. 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 kernels. Ann. Inst. Henri Poincaré C Anal. Non Linéaire (2022). [Google Scholar]
  30. G.M. Coclite, N. De Nitti, A. Keimer and L. Pflug, On existence and uniqueness of weak solutions to nonlocal conservation laws with BV kernels. Z. Angew. Math. Phys. 73 (2022) 10. [CrossRef] [Google Scholar]
  31. R.M. Colombo and M. Lécureux-Mercier, Nonlocal crowd dynamics models for several populations. Acta Math. Sci. Ser. B (Engl. Ed.) 32 (2012) 177–196. [MathSciNet] [Google Scholar]
  32. R.M. Colombo, M. Herty and M. Mercier, Control of the continuity equation with a non local flow. ESAIM Control Optim. Calc. Var. 17 (2011) 353–379. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  33. R.M. Colombo, M. Garavello and M. Lécureux-Mercier, A class of nonlocal models for pedestrian traffic. Math. Models Methods Appl. Sci. 22 (2012) 34. [Google Scholar]
  34. M. Colombo, G. Crippa and L.V. Spinolo, On the singular local limit for conservation laws with nonlocal fluxes. Arch. Ration. Mech. Anal. 233 (2019) 1131–1167. [CrossRef] [MathSciNet] [Google Scholar]
  35. M. Colombo, G. Crippa, M. Graff and L.V. Spinolo, On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws. ESAIM Math. Model. Numer. Anal. 55 (2021) 2705–2723. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  36. 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 C Anal. Non Linéaire 38 (2021) 1653–1666. [CrossRef] [MathSciNet] [Google Scholar]
  37. M. Colombo, G. Crippa, E. Marconi and L.V. Spinolo, Nonlocal traffic models with general kernels: singular limit, entropy admissibility, and convergence rate. Arch. Ration. Mech. Anal. 247 (2023) 32. [CrossRef] [Google Scholar]
  38. C. De Filippis and P. Goatin, The initial-boundary value problem for general non-local scalar conservation laws in one space dimension. Nonlinear Anal. 161 (2017) 131–156. [Google Scholar]
  39. Q. Du, Z. Huang and P.G. LeFloch, Nonlocal conservation laws. A new class of monotonicity-preserving models. SIAM J. Numer. Anal. 55 (2017) 2465–2489. [CrossRef] [MathSciNet] [Google Scholar]
  40. U.S. Fjordholm and A.M. Ruf, Second-order accurate TVD numerical methods for nonlocal nonlinear conservation laws. SIAM J. Numer. Anal. 59 (2021) 1167–1194. [CrossRef] [MathSciNet] [Google Scholar]
  41. J. Friedrich and O. Kolb, Maximum principle satisfying CWENO schemes for nonlocal conservation laws. SIAM J. Sci. Comput. 41 (2019) A973–A988. [CrossRef] [Google Scholar]
  42. 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]
  43. J. Friedrich, S. Göttlich and E. Rossi, Nonlocal approaches for multilane traffic models. Commun. Math. Sci. 19 (2021) 2291–2317. [CrossRef] [MathSciNet] [Google Scholar]
  44. J. Friedrich, S. Göttlich and M. Osztfalk, Network models for nonlocal traffic flow. ESAIM Math. Model. Numer. Anal. 56 (2022) 213–235. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  45. J. Friedrich, S. Sudha and S. Rathan, Numerical schemes for a class of nonlocal conservation laws: a general approach. Netw. Heterog. Media 18 (2023) 1335–1354. [CrossRef] [MathSciNet] [Google Scholar]
  46. 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]
  47. P. Goatin and E. Rossi, Well-posedness of IBVP for 1D scalar non-local conservation laws. ZAMM Z. Angew. Math. Mech. 99 (2019) 26. [CrossRef] [Google Scholar]
  48. E. Godlewski and P.-A. Raviart, Hyperbolic systems of conservation laws. In Vol. 3/4 of Mathématiques & Applications (Paris) [Mathematics and Applications]. Ellipses, Paris (1991). [Google Scholar]
  49. S. Göttlich, S. Hoher, P. Schindler, V. Schleper and A. Verl, Modeling, simulation and validation of material flow on conveyor belts. Appl. Math. Model. 38 (2014) 3295–3313. [Google Scholar]
  50. S. Gottlieb and C.-W. Shu, Total variation diminishing runge-kutta schemes. Math. Comput. 67 (1998) 73–85. [NASA ADS] [CrossRef] [Google Scholar]
  51. S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (2001) 89–112. [Google Scholar]
  52. V. Gowda and J. Jaffré, A discontinuous finite element method for scalar nonlinear conservation laws. Rapp. Rech. INRIA 1848 (1993). [Google Scholar]
  53. H. Holden and N.H. Risebro, Front tracking for hyperbolic conservation laws. Springer Berlin, Heidelberg (2015) 2. [Google Scholar]
  54. K. Huang and Q. Du, Stability of a nonlocal traffic flow model for connected vehicles. SIAM J. Appl. Math. 82 (2022) 221–243. [CrossRef] [MathSciNet] [Google Scholar]
  55. K. Huang and Q. Du, Asymptotically compatibility of a class of numerical schemes for a nonlocal traffic flow model. Preprint arXiv:2301.00803 (2023). [Google Scholar]
  56. K.H. Karlsen, N.H. Risebro and J.D. Towers, L1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Skr. K. Nor. Vidensk. Selsk. (2003) 1–49. [Google Scholar]
  57. A. Keimer ans L. Pflug, Existence, uniqueness and regularity results on nonlocal balance laws. J. Differ. Equ. 263 (2017) 4023–4069. [CrossRef] [Google Scholar]
  58. A. Keimer and L. Pflug, On approximation of local conservation laws by nonlocal conservation laws. J. Math. Anal. Appl. 475 (2019) 1927–1955. [CrossRef] [MathSciNet] [Google Scholar]
  59. A. Keimer, L. Pflug and M. Spinola, Existence, uniqueness and regularity of multi-dimensional nonlocal balance laws with damping. J. Math. Anal. Appl. 466 (2018) 18–55. [Google Scholar]
  60. P. Lax and B. Wendroff, Systems of conservation laws. Comm. Pure Appl. Math. 13 (1960) 217–237. [CrossRef] [Google Scholar]
  61. A.Y. Le Roux, Convergence of an accurate scheme for first order quasilinear equations. RAIRO Anal. Numér. 15 (1981) 151–170. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  62. B. Perthame, Transport equations in biology. Frontiers in Mathematics, Birkhäuser Verlag, Basel (2007). [Google Scholar]
  63. J. Ridder and W. Shen, Traveling waves for nonlocal models of traffic flow. Discrete Contin. Dyn. Syst. 39 (2019) 4001–4040. [CrossRef] [MathSciNet] [Google Scholar]
  64. E. Rossi, J. Weißen, P. Goatin and S. Göttlich, Well-posedness of a non-local model for material flow on conveyor belts. ESAIM Math. Model. Numer. Anal. 54 (2020) 679–704. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  65. W. Shen, Traveling waves for conservation laws with nonlocal flux for traffic flow on rough roads. Netw. Heterog. Media 14 (2019) 709–732. [CrossRef] [MathSciNet] [Google Scholar]
  66. C.-W. Shu and S. Osher, Efficient implementation of essentially nonoscillatory shock-capturing schemes. J. Comput. Phys. 77 (1988) 439–471. [NASA ADS] [CrossRef] [Google Scholar]
  67. A. Sopasakis and M.A. Katsoulakis, Stochastic modeling and simulation of traffic flow: asymmetric single exclusion process with Arrhenius look-ahead dynamics. SIAM J. Appl. Math. 66 (2006) 921–944. [CrossRef] [MathSciNet] [Google Scholar]
  68. B. van Leer, Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov’s method. J. Comput. Phys. 32 (1979) 101–136. [CrossRef] [Google Scholar]
  69. B. van Leer, On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe. SIAM J. Sci. Statist. Comput. 5 (1984) 1–20. [CrossRef] [MathSciNet] [Google Scholar]
  70. B. van Leer, Upwind and high-resolution methods for compressible flow: From donor cell to residual-distribution schemes. Commun. Comput. Phys. 1 (2006) 192–206. [Google Scholar]
  71. M.-C. Viallon, Convergence of the two-point upstream weighting scheme. Math. Comp. 57 (1991) 569–584. [CrossRef] [MathSciNet] [Google Scholar]
  72. J.-P. Vila, High-order schemes and entropy condition for nonlinear hyperbolic systems of conservation laws. Math. Comp. 50 (1988) 53–73. [CrossRef] [MathSciNet] [Google Scholar]
  73. J.-P. Vila, An analysis of a class of second-order accurate Godunov-type schemes. SIAM J. Numer. Anal. 26 (1989) 830–853. [CrossRef] [MathSciNet] [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