Free Access
Volume 27, 2021
Article Number 28
Number of page(s) 35
Published online 30 March 2021
  1. D. Alexander, I. Kim and Y. Yao, Quasi-static evolution and congested crowd transport. Nonlinearity 27 (2014) 823–858. [Google Scholar]
  2. J.-D. Benamou, G. Carlier and M. Laborde, An augmented Lagrangian approach to Wasserstein gradient flows and applications. ESAIM: PROC. 54 (2016) 1–17. [Google Scholar]
  3. J.-D. Benamou, G. Carlier, Q. Mérigot and É. Oudet, Discretization of functionals involving the Monge–Ampère operator. Numer. Math. 134 (2016) 611–636. [Google Scholar]
  4. M. Burger, J.A. Carrillo and M.-T. Wolfram, A mixed finite element method for nonlinear diffusion equations. Kinet. Relat. Models 3 (2010) 59–83. [CrossRef] [MathSciNet] [Google Scholar]
  5. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 44 (1991) 375–417. [Google Scholar]
  6. J.A. Carrillo, K. Craig, L. Wang and C. Wei, Primal dual methods for Wasserstein gradient flows. Preprint arXiv:1901.08081 (2019). [Google Scholar]
  7. G. Carlier, V. Duval, G. Peyré and B. Schmitzer, Convergence of entropic schemes for optimal transport and gradient flows. SIAM J. Math. Anal. 49 (2017) 1385–1418. [Google Scholar]
  8. J.A. Carrillo and J.S. Moll, Numerical simulation of diffusive and aggregation phenomena in nonlinear continuity equations by evolving diffeomorphisms. SIAM J. Sci. Comput. 31 (2009/10) 4305–4329. [Google Scholar]
  9. J.A. Carrillo, L. Wang, W. Xu and M. Yan, Variational asymptotic preserving scheme for the Vlasov–Poisson–Fokker–Planck system. Preprint arXiv:2007.01969 (2020). [Google Scholar]
  10. G. De Philippis, A. Richárd Mészáros, F. Santambrogio and B. Velichkov, BV estimates in optimal transportation and applications. Arch. Ration. Mech. Anal. 219 (2016) 829–860. [Google Scholar]
  11. L.C. Evans, Partial differential equations. Vol. 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, second edition (2010) 829–860. [Google Scholar]
  12. D.J. Eyre, Unconditionally gradient stable time marching the Cahn–Hilliard equation. MRS Proc. 529 (1998) 39. [Google Scholar]
  13. W. Gangbo, An elementary proof of the polar factorization of vector-valued functions. Arch. Ratl. Mech. Anal. 128 (1994) 381–399. [Google Scholar]
  14. W. Gangbo, Quelques problemes d’analyse non convexe. Habilitation à diriger des recherches en mathématiques. Université de Metz (1995). [Google Scholar]
  15. W. Gangbo, Quelques problèmes d’analyse non convexe. Habilitation à diriger des recherches en mathématiques. Habilitation, Université de Metz (January 1995). [Google Scholar]
  16. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113–161. [Google Scholar]
  17. G. Isaakovich Barenblatt Scaling, self-similarity, and intermediate asymptotics. With a foreword by Ya. B. Zeldovich. Vol. 14 of Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (1996). [Google Scholar]
  18. G. Isaakovich Barenblatt, Scaling. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2003). With a foreword by Alexandre Chorin. [Google Scholar]
  19. R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker–Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17. [Google Scholar]
  20. M. Jacobs, I. Kim and J. Tong, The L1-contraction principle in optimal transport. Preprint arXiv:2006.09557 (2020). [Google Scholar]
  21. M. Jacobs and F. Léger, A fast approach to optimal transport: the back-and-forth method. Numer. Math. 146 (2020) 513–544. [Google Scholar]
  22. H. Leclerc, Q. Mérigot, F. Santambrogio and F. Stra, Lagrangian discretization of crowd motion and linear diffusion. SIAM J. Numer. Anal. 58 (2020) 2093–2118. [Google Scholar]
  23. Y. Lucet, Faster than the fast Legendre transform, the linear-time Legendre transform. Numer. Algor. 16 (1997) 171–185. [Google Scholar]
  24. Y. Nesterov, Vol. 87 of Introductory lectures on convex optimization: A basic course. Springer Science & Business Media (2013). [Google Scholar]
  25. F. Otto, The geometry of dissipative evolution equations: the porous medium equation. Commun. Partial Differ. Equ. 26 (2001) 101–174. [Google Scholar]
  26. G. Peyré, Entropic approximation of Wasserstein gradient flows. SIAM J. Imag. Sci. 8 (2015) 2323–2351. [CrossRef] [Google Scholar]
  27. F. Santambrogio, Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling. Vol. 87 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser/Springer, Cham (2015). [CrossRef] [Google Scholar]
  28. J.L. Vázquez, The porous medium equation: mathematical theory. Oxford University Press (2007). [Google Scholar]

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