Open Access
Volume 58, Number 2, March-April 2024
Page(s) 759 - 792
Published online 19 April 2024
  1. V. Anaya, M. Bendahmane and M. Sepúlveda, Numerical analysis for a three interacting species model with nonlocal and cross diffusion. ESAIM:M2AN 49 (2015) 171–192. [Google Scholar]
  2. N. Ayi, M. Herda, H. Hivert and I. Tristani, On a structure-preserving numerical method for fractional Fokker–Planck equations. Math. Comput. 92 (2023) 635–693. [Google Scholar]
  3. M. Bendahmane and M. Sepúlveda, Convergence of a finite volume scheme for nonlocal reaction-diffusion systems modelling an epidemic disease. Discrete Contin. Dyn. Syst. B 11 (2009) 823–853. [Google Scholar]
  4. M. Bertsch, M.E. Gurtin, D. Hilhorst and L.A. Peletier, On interacting populations that disperse to avoid crowding: preservation of segregation. J. Math. Biol. 23 (1985) 1–13. [Google Scholar]
  5. 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]
  6. J.A. Carrillo, A. Chertock and Y. Huang, A finite-volume method for nonlinear nonlocal equations with a gradient flow structure. Commun. Comput. Phys. 17 (2015) 233–258. [Google Scholar]
  7. 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]
  8. J.A. Carrillo, F. Filbet and M. Schmidtchen, Convergence of a finite volume scheme for a system of interacting species with cross-diffusion. Numer. Math. 145 (2020) 473–511. [Google Scholar]
  9. C. Chainais-Hillairet, J.-G. Liu and Y.-J. Peng, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. ESAIM:M2AN 37 (2003) 319–338. [Google Scholar]
  10. L. Chen, E. Daus and A. Jüngel, Rigorous mean-field limit and cross diffusion. Z. Angew. Math. Phys. 70 (2019) 21. [Google Scholar]
  11. K. Deimling, Nonlinear Functional Analysis. Springer, Berlin (1985). [Google Scholar]
  12. H. Dietert and A. Moussa, Persisting entropy structure for nonlocal cross-diffusion systems. To appear in Ann. Fac. Sci. Toulouse (2024) Preprint: arXiv:2101.02893. [Google Scholar]
  13. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods, edited by P.G. Ciarlet and J.-L. Lions. In: Handbook of Numerical Analysis 7 (2000) 713–1018. [Google Scholar]
  14. G. Galiano, Error analysis of some nonlocal diffusion discretization schemes. Comput. Math. Appl. 103 (2021) 40–52. [Google Scholar]
  15. T. Gallouët and J.-C. Latché, Compactness of discrete approximate solutions to parabolic PDEs–Application to a turbulence model. Commun. Pure Appl. Anal. 11 (2012) 2371–2391. [Google Scholar]
  16. M. Herda and A. Moussa, Matlab code for “Study of a structure preserving finite volume scheme for a nonlocal cross-diffusion system” (2022). [Google Scholar]
  17. M. Herda and A. Moussa, Study of a structure preserving finite volume scheme for a nonlocal cross-diffusion system. ESAIM:M2AN 57 (2023) 1589–1617. [Google Scholar]
  18. A. Jüngel and A. Zurek, A convergent structure-preserving finite-volume scheme for the Shigesada–Kawasaki–Teramoto population system. SIAM J. Numer. Anal. 59 (2021) 2286–2309. [Google Scholar]
  19. A. Jüngel, S. Portisch and A. Zurek. Nonlocal cross-diffusion systems for multi-species populations and networks. Nonlinear Anal. 219 (2022) 26. [Google Scholar]
  20. A. Jüngel, S. Portisch and A. Zurek, Matlab code for “A convergent finite-volume scheme for nonlocal cross-diffusion systems for multi-species populations” (2023). [Google Scholar]
  21. G. Medvedev and G. Moussa, A numerical method for a nonlocal diffusion equation with additive noise. Stoch. PDE: Anal. Comput. 11 (2023) 1433–1469. [Google Scholar]
  22. J.R. Potts and M.A. Lewis, Spatial memory and taxis-driven pattern formation in model ecosystems. Bull. Math. Biol. 81 (2019) 2725–2747. [Google Scholar]
  23. C. Rao, Diversity and dissimilarity coefficients: a unified approach. Theor. Popul. Biol. 21 (1982) 24–43. [Google Scholar]
  24. F. Santambrogio, Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling. Prog. Nonlinear Differ. Equ. Appl. Cham, Birkh¨auser, Springer (2015). [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