EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 20 (2025) Math. Model. Nat. Phenom., 20 (2025) 10 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 20, 2025
Article Number 10
Number of page(s) 28
Section Mathematical methods
DOI https://doi.org/10.1051/mmnp/2025011
Published online 16 April 2025
  1. C. Castellano, S. Fortunato and V. Loreto, Statistical physics of social dynamics. Rev. Mod. Phys. 81 (2009) 591-646. [Google Scholar]
  2. C.M. Dafermos, Hyperbolic conservation laws in continuum physics. Vol. 325 of Grundlehren der mathematischen Wissenschaften, 4th edn. Springer-Verlag, Berlin (2016). [CrossRef] [Google Scholar]
  3. R.M. Colombo and A. Marson, A Holder continuous ODE related to traffic flow. Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 759-772. [CrossRef] [MathSciNet] [Google Scholar]
  4. U.S. Fjordholm, O.H. Mæhlen and M.C. Orke, The particle paths of hyperbolic conservation laws. Math. Models Methods Appl. Sci. 34 (2024) 1205-1234. [Google Scholar]
  5. M. Di Francesco and M.D. Rosini, Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit. Arch. Ration. Mech. Anal. 217 (2015) 831-871. [Google Scholar]
  6. H. Holden and N.H. Risebro, The continuum limit of Follow-the-Leader models—a short proof. Discrete Contin. Dyn. Syst. 38 (2018) 715-722. [Google Scholar]
  7. J. Weissen, S. Göttlich and D. Armbruster, Density dependent diffusion models for the interaction of particle ensembles with boundaries. Kinet. Relat. Models 14 (2021) 681-704. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Cucker and S. Smale, Emergent behavior in flocks. IEEE Trans. Automat. Control 52 (2007) 852-862. [CrossRef] [MathSciNet] [Google Scholar]
  9. G. Aletti, G. Naldi and G. Toscani, First-order continuous models of opinion formation. SIAM J. Appl. Math. 67 (2007) 837-853. [Google Scholar]
  10. R. Burger, 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. [Google Scholar]
  11. R.M. Colombo, M. Garavello and M. Lecureux-Mercier, A class of nonlocal models for pedestrian traffic. Math. Models Methods Appl. Sci. 22 (2012) 1150023. [Google Scholar]
  12. D. Amadori and C. Christoforou, BV solutions for a hydrodynamic model of flocking-type with all-to-all interaction kernel. Math. Models Methods Appl. Sci. 32 (2022) 2295-2357. [Google Scholar]
  13. J.A. Carrillo, D. Gómez-Castro and J.L. Vazquez, Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility. Adv. Nonlinear Anal. 11 (2022) 937-967. [Google Scholar]
  14. S. Fagioli and O. Tse, On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility. Nonlinear Anal. 221 (2022) Paper No. 112904, 35. [Google Scholar]
  15. A. Bayliss and V.A. Volpert, Patterns for competing populations with species specific nonlocal coupling. Math. Model. Nat. Phenom. 10 (2015) 30-47. [Google Scholar]
  16. R. Eftimie, The effect of different communication mechanisms on the movement and structure of self-organised aggregations. Math. Model. Nat. Phenom. 8 (2013) 5-24. [Google Scholar]
  17. C. Dull, P. Gwiazda, A. Marciniak-Czochra and J. Skrzeczkowski, Structured population models on Polish spaces: a unified approach including graphs, Riemannian manifolds and measure spaces to describe dynamics of heterogeneous populations. Math. Models Methods Appl. Sci. 34 (2024) 109-143. [Google Scholar]
  18. R.M. Colombo, M. Garavello and C. Nocita, General stability estimates in nonlocal traffic models for several populations. NoDEA, Nonlinear Differ. Equ. Appl. 32 (2025) 34. [Google Scholar]
  19. G. Crippa and M. Lecureux-Mercier, Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow. Nonlinear Diff. Equ. Appl. 20 (2013) 523-537. [Google Scholar]
  20. H. Brezis, Analyse fonctionnelle. Collection Mathematiques Appliquees pour la Maîtrise. Masson, Paris (1983). Theorie et applications. [Google Scholar]
  21. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2002). [CrossRef] [Google Scholar]
  22. 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]
  23. M. Burger, R. Pinnau, C. Totzeck, O. Tse and A. Roth, Instantaneous control of interacting particle systems in the mean-field limit. J. Comput. Phys. 405 (2020) 109181, 20. [Google Scholar]
  24. A. Keimer and L. Pflug, Chapter 6 - Nonlocal balance laws -— an overview over recent Results, in Numerical Control: Part B. Vol. 24 of Handbook of Numerical Analysis, edited by E. Trélat and E. Zuazua. Elsevier (2023) 183-216. [Google Scholar]
  25. A. Keimer and L. Pflug, Discussion. (2024). [Google Scholar]
  26. R.M. Colombo and A. Salvadori, Non conservative and non local dynamics of clusters. (2024) In preparation. [Google Scholar]
  27. S.N. KruZkov, First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81 (1970) 228-255. [MathSciNet] [Google Scholar]
  28. R.M. Colombo and E. Rossi, Well-posedness and control in a hyperbolic-parabolic parasitoid-parasite system. Stud. Appl. Math. 147 (2021) 839-871. [Google Scholar]
  29. R.J. DiPerna and P.L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989) 511-547. [Google Scholar]
  30. F.H. Clarke, Optimization and nonsmooth analysis. Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wiley & Sons, Inc., New York (1983). [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.