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All issues Volume 57 / No 3 (May-June 2023) ESAIM: M2AN, 57 3 (2023) 1589-1617 References
Open Access
Issue
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
Page(s) 1589 - 1617
DOI https://doi.org/10.1051/m2an/2023032
Published online 26 May 2023
  1. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Clarendon Press, Oxford (2000). [Google Scholar]
  2. V. Anaya, M. Bendahmane, M. Langlais and M. Sepúlveda, A convergent finite volume method for a model of indirectly transmitted diseases with nonlocal cross-diffusion. Comput. Math. Appl. 70 (2015) 132–157. [CrossRef] [MathSciNet] [Google Scholar]
  3. V. Anaya, M. Bendahmane and M. Sepúlveda, Numerical analysis for a three interacting species model with nonlocal and cross diffusion. ESAIM: Math. Model. Numer. Anal. 49 (2015) 171–192. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  4. B. Andreianov, M. Bendahmane and R. Ruiz-Baier, Analysis of a finite volume method for a cross-diffusion model in population dynamics. Math. Models Methods Appl. Sci. 21 (2011) 307–344. [CrossRef] [MathSciNet] [Google Scholar]
  5. J. Baladron, D. Fasoli, O. Faugeras and J. Touboul, Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh–Nagumo neurons. J. Math. Neurosci. 2 (2012) 50. [CrossRef] [Google Scholar]
  6. M. Bessemoulin-Chatard, M. Herda and T. Rey, Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations. Math. Comput. 89 (2020) 1093–1133. [Google Scholar]
  7. M. Braukhoff, I. Perugia and P. Stocker, An entropy structure preserving space-time formulation for cross-diffusion systems: analysis and galerkin discretization. SIAM J. Num. Anal. 60 (2022) 364–395. [CrossRef] [Google Scholar]
  8. M. Burger, M. Di Francesco, J.-F. Pietschmann and B. Schlake, Nonlinear cross-diffusion with size exclusion. SIAM J. Math. Anal. 42 (2010) 2842–2871. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Burger, J.A. Carrillo, J.-F. Pietschmann and M. Schmidtchen, Segregation effects and gap formation in cross-diffusion models. Interfaces Free Bound. 22 (2020) 175–203. [CrossRef] [MathSciNet] [Google Scholar]
  10. C. Cancès and B. Gaudeul, A convergent entropy diminishing finite volume scheme for a cross-diffusion system. SIAM J. Numer. Anal. 58 (2020) 2684–2710. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Cancès, C. Chainais-Hillairet, A. Gerstenmayer and A. Jüngel, Finite-volume scheme for a degenerate cross-diffusion model motivated from ion transport. Numer. Methods Part. Differ. Equ. 35 (2019) 545–575. [CrossRef] [Google Scholar]
  12. 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. [CrossRef] [MathSciNet] [Google Scholar]
  13. 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]
  14. 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. [CrossRef] [MathSciNet] [Google Scholar]
  15. C. Chainais-Hillairet and M. Herda, Large-time behaviour of a family of finite volume schemes for boundary-driven convection-diffusion equations. IMA J. Numer. Anal. 40 (2020) 2473–2504. [CrossRef] [MathSciNet] [Google Scholar]
  16. C. Chainais-Hillairet, M. Herda, S. Lemaire and J. Moatti, Long-time behaviour of hybrid finite volume schemes for advection–diffusion equations: linear and nonlinear approaches. Numer. Math. 151 (2022) 963–1016. [CrossRef] [MathSciNet] [Google Scholar]
  17. L. Chen and A. Jüngel, Analysis of a multidimensional parabolic population model with strong cross-diffusion. SIAM J. Math. Anal. 36 (2004) 301–322. [CrossRef] [MathSciNet] [Google Scholar]
  18. L. Chen and A. Jüngel, Analysis of a parabolic cross-diffusion population model without self-diffusion. J. Differ. Equ. 224 (2006) 39–59. [CrossRef] [Google Scholar]
  19. L. Chen, E.S. Daus, A. Holzinger and A. Jüngel, Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems. J. Nonlinear Sci. 31 (2021) 38. [CrossRef] [Google Scholar]
  20. L. Desvillettes, T. Lepoutre, A. Moussa and A. Trescases, On the entropic structure of reaction-cross diffusion systems. Commun. Part. Differ. Equ. 40 (2015) 1705–1747. [CrossRef] [Google Scholar]
  21. H. Dietert and A. Moussa, Persisting entropy structure for nonlocal cross-diffusion systems. Preprint arXiv:2101.02893 (2021). [Google Scholar]
  22. P. Domschke, D. Trucu, A. Gerisch and M. Chaplain, Mathematical modelling of cancer invasion: implications of cell adhesion variability for tumour infiltrative growth patterns. J. Theor. Biol. 361 (2014) 41–60. [CrossRef] [Google Scholar]
  23. B. Düring, P. Markowich, J.-F. Pietschmann and M.-T. Wolfram, Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proc. R. Soc. Lond. Ser. A, Math. Phys. Eng. Sci. 465 (2009) 3687–3708. [MathSciNet] [Google Scholar]
  24. L.C. Evans, Partial Differential Equations. Vol. 19 of Grad. Stud. Math., 2nd edition. American Mathematical Society (AMS), Providence, RI (2010). [Google Scholar]
  25. F. Filbet and M. Herda, A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure. Numer. Math. 137 (2017) 535–577. [CrossRef] [MathSciNet] [Google Scholar]
  26. J. Fontbona and S. Méléard, Non local Lotka-Volterra system with cross-diffusion in an heterogeneous medium. J. Math. Biol. 70 (2015) 829–854. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. G. Galiano, M. Garzón and A. Jüngel, Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model. Numer. Math. 93 (2003) 655–673. [CrossRef] [MathSciNet] [Google Scholar]
  28. V. Giunta, T. Hillen, M.A. Lewis and J.R. Potts, Local and global existence for non-local multi-species advection–diffusion models. SIAM J. Appl. Dyn. Syst. 21 (2022) 1686–1708. [CrossRef] [MathSciNet] [Google Scholar]
  29. A. Jüngel, The boundedness-by-entropy method for cross-diffusion systems. Nonlinearity 28 (2015) 1963–2001. [CrossRef] [MathSciNet] [Google Scholar]
  30. A. Jüngel, Entropy Methods for Diffusive Partial Differential Equations. Springer, Cham; BCAM – Basque Center for Applied Mathematics, Bilbao (2016). [Google Scholar]
  31. 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. [CrossRef] [MathSciNet] [Google Scholar]
  32. A. Jüngel, S. Portisch and A. Zurek, Nonlocal cross-diffusion systems for multi-species populations and networks. Nonlin. Anal. 219 (2022) 112800. [CrossRef] [Google Scholar]
  33. S.N. Kruzhkov, Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications. Math. Notes Acad. Sci. USSR 6 (1969) 517–523. [Google Scholar]
  34. T. Lepoutre and A. Moussa, Entropic structure and duality for multiple species cross-diffusion systems. Nonlinear Anal. Theory Methods Appl. Ser. A Theory Methods 159 (2017) 298–315. [CrossRef] [Google Scholar]
  35. S.A. Levin and L.A. Segel, Hypothesis for origin of planktonic patchiness. Nature 259 (1976) 659–659. [CrossRef] [PubMed] [Google Scholar]
  36. M. Mimura, Y. Nishiura and M. Yamaguti, Some diffusive prey and predator systems and their bifurcation problems. Ann. New York Acad. Sci. 316 (1979) 490–510. [CrossRef] [Google Scholar]
  37. A. Moussa, From nonlocal to classical Shigesada–Kawasaki–Teramoto systems: triangular case with bounded coefficients. SIAM J. Math. Anal. 52 (2020) 42–64. [CrossRef] [MathSciNet] [Google Scholar]
  38. H. Murakawa and H. Togashi, Continuous models for cell-cell adhesion. J. Theor. Biol. 374 (2015) 1–12. [CrossRef] [Google Scholar]
  39. K.J. Painter, J.M. Bloomfield, J.A. Sherratt and A. Gerisch, A nonlocal model for contact attraction and repulsion in heterogeneous cell populations. Bull. Math. Biol. 77 (2015) 1132–1165. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  40. J.R. Potts and M.A. Lewis, Spatial memory and taxis-driven pattern formation in model ecosystems. Bull. Math. Biol. 81 (2019) 2725–2747. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  41. F. Rellich, Ein Satz über mittlere Konvergenz. Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. (1930) 30–35. [Google Scholar]
  42. N. Shigesada, K. Kawasaki and E. Teramoto, Spatial segregation of interacting species. J. Theor. Biol. 79 (1979) 83–99. [CrossRef] [Google Scholar]
  43. Z. Sun, J.A. Carrillo and C.-W. Shu, An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems. Kinet. Relat. Models 12 (2019) 885–908. [CrossRef] [MathSciNet] [Google Scholar]

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