EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 59 / No 6 (November-December 2025) ESAIM: M2AN, 59 6 (2025) 3301-3340 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
Page(s) 3301 - 3340
DOI https://doi.org/10.1051/m2an/2025092
Published online 17 December 2025
  1. D. Albritton and L. Ohm, On the stabilizing effect of swimming in an active suspension. SIAM J. Math. Anal. 55 (2023) 6093–6132. [Google Scholar]
  2. R. Alert, J. Casademunt and J.-F. Joanny, Active turbulence. Ann. Rev. Condens. Matter Phys. 13 (2022) 143–170. [Google Scholar]
  3. K.A. Bacik, B.S. Bacik and T. Rogers, Lane nucleation in complex active flows. Science 379 (2023) 923–928. [Google Scholar]
  4. R. Bailo, J.A. Carrillo, H. Murakawa and M. Schmidtchen, Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations. Math. Models Methods Appl. Sci. 30 (2020) 2487–2522. [Google Scholar]
  5. N. Bellomo, P. Degond and E. Tadmor, editors, Active Particles, Volume 1. Advances in Theory, Models, and Applications. Model. Simul. Sci. Eng. Technol. Birkh¨auser/Springer, Basel (2017). [Google Scholar]
  6. N. Bellomo, P. Degond and E. Tadmor, editors, Active Particles, Volume 2. Model. Simul. Sci. Eng. Technol. Birkh¨auser, Cham (2019). [Google Scholar]
  7. N. Bellomo, J.A. Carrillo and E. Tadmor, editors, Active Particles. Volume 3. Advances in Theory, Models, and Applications. Model. Simul. Sci. Eng. Technol. Birkh¨auser, Cham (2022). [Google Scholar]
  8. C. Bertucci, M. Rakotomalala and M. Tomasevic, Curvature in chemotaxis: a model for ant trail pattern formation. Preprint arXiv:2408.13363 (2024). [Google Scholar]
  9. M. Bessemoulin-Chatard, C. Chainais-Hillairet and F. Filbet, On discrete functional inequalities for some finite volume schemes. IMA J. Numer. Anal. 35 (2015) 1125–1149. [Google Scholar]
  10. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, 1 edition. Springer, New York, NY, USA (2010). [Google Scholar]
  11. M. Briant, A. Diez and S. Merino-Aceituno, Cauchy theory for general kinetic Vicsek models in collective dynamics and mean-field limit approximations. SIAM J. Math. Anal. 54 (2022) 1131–1168. [Google Scholar]
  12. M. Bruna, M. Burger, A. Esposito and S.M. Schulz, Phase separation in systems of interacting active Brownian particles. SIAM J. Appl. Math. 82 (2022) 1635–1660. [Google Scholar]
  13. M. Bruna, M. Burger and O. de Wit, Lane formation and aggregation spots in a model of ants. SIAM J. Appl. Dyn. Syst. 24 (2025) 675–709. [Google Scholar]
  14. M. Burger and S. Schulz, Well-posedness and stationary states for a crowded active Brownian system with size-exclusion. Preprint arXiv:2309.17326 (2023). [Google Scholar]
  15. M. Burger, S. Hittmeir, H. Ranetbauer and M.-T. Wolfram, Lane formation by side-stepping. SIAM J. Math. Anal. 48 (2016) 981–1005. [Google Scholar]
  16. J.A. Carrillo, Y. Huang and M. Schmidtchen, Zoology of a nonlocal cross-diffusion model for two species. SIAM J. Appl. Math. 78 (2018) 1078–1104. [Google Scholar]
  17. J.A. Carrillo, R.S. Gvalani and J.S.-H. Wu, An invariance principle for gradient flows in the space of probability measures. J. Differ. Equ. 345 (2023) 233–284. [Google Scholar]
  18. C. Chainais-Hillairet and F. Filbet, Asymptotic behaviour of a finite-volume scheme for the transient drift-diffusion model. IMA J. Numer. Anal. 27 (2007) 689–716. [CrossRef] [MathSciNet] [Google Scholar]
  19. C. Chainais-Hillairet, J.-G. Liu and Y.-J. Peng, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. ESAIM: Math. Model. Numer. Anal. 37 (2003) 319–338. [Google Scholar]
  20. O. de Wit, Numerics ants, Last accessed 25 March 2025. https://github.com/odewit8/numerics_ants (2025). [Google Scholar]
  21. P. Degond, A. Frouvelle and J.-G. Liu, Macroscopic limits and phase transition in a system of self-propelled particles. J. Nonlinear Sci. 23 (2013) 427–456. [Google Scholar]
  22. L.C. Evans, Partial Differential Equations, 2 edition. American Mathematical Society (2010). [Google Scholar]
  23. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods. Handb. Numer. Anal. 7 (2000) 713–1018. [Google Scholar]
  24. F. Filbet, A finite volume scheme for the Patlak–Keller–Segel chemotaxis model. Numer. Math. 104 (2006) 457–488. [Google Scholar]
  25. C.K. Hemelrijk and H. Hildenbrandt, Schools of fish and flocks of birds: their shape and internal structure by self-organization. Interface Focus 2 (2012) 726–737. [Google Scholar]
  26. R. Kowalczyk, Preventing blow-up in a chemotaxis model. J. Math. Anal. App. 305 (2005) 566–588. [Google Scholar]
  27. L. Ohm and M.J. Shelley, Weakly nonlinear analysis of pattern formation in active suspensions. J. Fluid Mech. 942 (2022) A53. [Google Scholar]
  28. K.J. Painter, P.K. Maini and H.G. Othmer, Stripe formation in juvenile pomacanthus explained by a generalized turing mechanism with chemotaxis. Proc. Nat. Acad. Sci. 96 (1999) 5549–5554. [Google Scholar]
  29. A. Perna, B. Granovskiy, S. Garnier, S.C. Nicolis, M. Labédan, G. Theraulaz, V. Fourcassié and D.J. Sumpter, Individual rules for trail pattern formation in argentine ants (Linepithema humile). PLoS Comput. Biol. 8 (2012) e1002592. [Google Scholar]
  30. A. Porretta, A note on the Sobolev and Gagliardo–Nirenberg inequality when p > n. Adv. Nonlinear Stud. 20 (2020) 361–371. [Google Scholar]
  31. J. Simon, Compact sets in the space lp(o, t; b). Annali di Matematica pura ed applicata 146 (1986) 65–96. [CrossRef] [Google Scholar]
  32. G. Zhou and N. Saito, Finite volume methods for a Keller–Segel system: discrete energy, error estimates and numerical blow-up analysis. Numer. Math. 135 (2017) 265–311. [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