Publications:

Preprints:

1. M. Di Francesco and V. Iorio, A system of continuity equations with nonlocal interactions of Morse type - Submitted preprint - PDF
2. M. Di Francesco, S. Fagioli, and E. Radici, Measure solutions, smoothing effect, and deterministic particle approximation for a conservation law with nonlocal flux - Submitted preprint - PDF on arXiv.org
3. M. Di Francesco, V. Iorio, and M. Schmidtchen, The approximation of the quadratic porous medium equation via nonlocal interacting particles subject to repulsive Morse potential - Submitted preprint - PDF on arXiv.org

Published or forthcoming papers:

1. D. Amadori, B. Andreianov, M. Di Francesco, S. Fagioli, T. Girard, P. Goatin, P. Markowich, J.-F. Pietschmann, M. D. Rosini, G. Russo, G. Stivaletta, and M. T. Wolfram, The mathematical theory of Hughes' model: a survey of result In: Bellomo, N., Gibelli, L. (eds) Crowd Dynamics, Volume 4. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-46359-4_2 PDF on arXiv.org
2. M. Di Francesco, S. Fagioli, and V. Iorio, Second order two-species systems with nonlocal interactions: existence and large damping limits - Acta Applicandae Mathematicae volume 184, Article number: 9 (2023) - Published version
3. M. Di Francesco, S. Duisembay, D. Gomes and, R. Ribeiro, Particle approximation of one-dimensional Mean-Field-Games with local interactions - Discrete and Continuous Dynamical Systems July 2022, 42(7): 3569-3591 - Published version
4. M. Di Francesco and G. Stivaletta, The one-sided Lipschitz condition in the follow-the-leader approximation of scalar conservation laws. - J. Hyperbolic Differ. Equ. 19, no. 4, 775–807 (2022). - Published version
5. M. Di Francesco, A. Esposito, and M. Schmidtchen, Many-particle limit for a system of interaction equations driven by Newtonian potentials. - Calc. Var. PDE (2021) 60:68 - Published version
6. M. Di Francesco and G. Stivaletta, Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux. - Discrete and Continuous Dynamical Systems 40 (1), 233-266 (2020) - Published version
7. J. A. Carrillo, M. Di Francesco, A. Esposito, S. Fagioli, and M. Schmidtchen, Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions. - Discrete and Continuous Dynamical Systems 40 (2), 1191-1231 (2020) - Published version
8. M. Di Francesco, S. Fagioli, and E. Radici, Deterministic particle approximation for nonlocal transport equations with nonlinear mobility - Journal of Differential Equations, 266 (5), 2830-2868 (2019) - Published version
9. M. Di Francesco and Y. Jaafra, Multiple large-time behavior of nonlocal interaction equations with quadratic diffusion - Kinetic and Related Models 12 (2), 303-322 (2019) - Published version
10. M. Burger, M. Di Francesco, S. Fagioli, and A. Stevens, Sorting Phenomena in a Mathematical Model For Two Mutually Attracting/Repelling Species - SIAM J. Math. Anal., 50 (3), 3210–3250 (2018) - Published version
11. M. Di Francesco, A. Esposito, and S. Fagioli, Nonlinear degenerate cross-diffusion systems with nonlocal interaction - Nonlinear Analysis, Volume 169, 94-117 (2018) - Published version
12. M. Di Francesco, S. Fagioli, M.D. Rosini, and G.Russo, A deterministic particle approximation for non-linear conservation laws. In Klingenberg C. and Westdickenberg M., editors, Theory Numerics and Applications of Hyperbolic Problems I, pages 487–499. Springer Proceedings in Mathematics & Statistics 236, (2018) - Published version.
13. M. Di Francesco, S. Fagioli, and M. D. Rosini, Deterministic particle approximation of scalar conservation laws - Bollettino dell'Unione Matematica Italiana, 10 (3), 487–501 (2017) - Published version
14. M. Di Francesco, S. Fagioli, M. D. Rosini, and G. Russo, Follow-the-leader approximations of macroscopic models for vehicular and pedestrian flows - Active Particles, Volume 1 (Springer), Editors: Nicola Bellomo, Pierre Degond, Eitan Tadmor, Part of the series Modeling and Simulation in Science, Engineering and Technology, pp 333-378 (2017) - Published version
15. M. Di Francesco, S. Fagioli, M. D. Rosini, and G. Russo, Deterministic particle approximation of the Hughes model in one space dimension - Kinetic and related models, 10 (1), 215-237 (2017) - Published version
16. M. Di Francesco, S. Fagioli, and M. D. Rosini, Many particle approximation for the Aw-Rascle-Zhang second order model for vehicular traffic - Mathematical Biosciences and Engineering, 14 (1), 127-141 (2016) - Published version
17. M. Di Francesco, Scalar conservation laws seen as gradient flows: known results and new perspectives - Gradient flows: from theory to application, 18–44, ESAIM Proc. Surveys, 54, EDP Sci., Les Ulis, (2016) - Published version
18. J. A. Carrillo, M. Di Francesco, and G. Toscani, Condensation phenomena in nonlinear drift equations- Ann. Sc. Norm. Super. Pisa Cl. Sci., (5) 15, 145-171 (2016) - Published version
19. M. Di Francesco and S. Fagioli, A nonlocal swarm model for predators–prey interactions - Mathematical Models and Methods in Applied Sciences, 26 (319), 319-355 (2016) - Published version
20. M. Di Francesco and M. D. Rosini, Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit - Archive for rational mechanics and analysis, 217 (3), 831-871 (2015) - Published version
21. G. A. Bonaschi, J. A. Carrillo, M. Di Francesco, and M. A. Peletier, Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D- ESAIM - Control, Optimisation and Calculus of Variations, 21 (2), 414-441 (2015) - Published version
22. M. Di Francesco, M. Fornasier, J.-C. Hütter, and D. Matthes, Asymptotic Behavior of Gradient Flows Driven by Nonlocal Power Repulsion and Attraction Potentials in One Dimension- SIAM Journal on Mathematical Analysis, 46 (6), 3814–3837 (2014) - Published version
23. M. Burger, M. Di Francesco, P. A. Markowich, and M.-T. Wolfram, Mean field games with nonlinear mobilities in pedestrian dynamics - Discrete and Continuous Dynamical Systems - B, 19, 1311 - 1333 (2014) - Published version
24. M. Di Francesco, and D. Matthes, Curves of steepest descent are entropy solutions for a class of degenerate convection-diffusion equations - Calc. Var. PDEs - 50, no. 1-2, 199–230 (2014) - Published version
25. M. Burger, M. Di Francesco, P. A. Markowich, and M.-T. Wolfram, On a mean field game optimal control approach modeling fast exit scenarios in human crowds, Proceedings of the IEEE Conference on Decision and Control, 52nd IEEE Conference on Decision and Control, 3128-3133 (2013) - Published version
26. M. Di Francesco, and S. Fagioli, Measure solutions for nonlocal interaction PDEs with two species - Nonlinearity 26, 2777-2808 (2013) - Published version
27. M. Burger, M. Di Francesco, and M. Franek, Stationary states of quadratic diffusion equations with long-range attraction - Commun. Math. Sci. 11, no. 3, 709–738 (2013) - Published version
28. D. Amadori, and M. Di Francesco, The one-dimensional Hughes model for pedestrian flow: Riemann--type solutions - Acta Mathematica Scientia 32 (1), 259-280 (2012) - Published version
29. J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, and D. Slepcev, Confinement in nonlocal interaction equations - Nonlinear Analysis 75, 550–558 (2012) - Published version
30. M. Di Francesco and M. Twarogowska, Asymptotic stability of constant steady states for a 2 x 2 reaction--diffusion system arising in cancer modelling - Mathematical and Computer modelling, 53 (7-8), 1457-1468 (2011) - Published version
31. J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, and D. Slepcev, Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations - Duke Mathematical Journal, 156 (2), 229-271 (2011) - Published version
32. M. Di Francesco, P. A. Markowich, J.-F. Pietschmann, and M.-T. Wolfram, On the Hughes' model for pedestrian flow: The one-dimensional case - Journal of Differential Equations, 250 (3), 1334-1362 (2011) - Published version
33. M. Burger, M. Di Francesco, J.-F. Pietschmann, and B. Schlake, Nonlinear Cross-Diffusion with Size Exclusion - SIAM J. Math. Anal. 42 (6), 2842-2871 (2010) - Published version
34. M. Di Francesco, A. Lorz, and P. A. Markowich, Chemotaxis fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior - Discrete and Continuous Dynamical Systems (A), 28 (4), 1437--1453 (2010) - Published version
35. M. Di Francesco and D. Donatelli, Singular convergence of nonlinear hyperbolic chemotaxis systems to Keller-Segel type models, Discrete and Continuous Dynamical Systems (B), 13 (1), 79-100 (2010) - Published version
36. M. Burger and M. Di Francesco, Large time behavior of nonlocal aggregation models with nonlinear diffusion, Networks and Heterogeneous Media, 3 (4), 749-785 (2008) - Published version
37. M. Di Francesco, K. Fellner, and P. A. Markowich, The entropy dissipation method for spatially inhomogeneous reaction-diffusion type systems, Proc. R. Soc. A 464, 3273-3300 (2008) - Published version
38. M. Di Francesco and J. Rosado, Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding, Nonlinearity 21, 2715–2730 (2008) - Published version
39. M. Di Francesco, K. Fellner, and H. Liu, A non-local conservation law with nonlinear "radiation" inhomogeneity, J. Hyperbolic Differ. Equ. 5, no. 1, 1-23 (2008) - Published version
40. M. Di Francesco, and M. Wunsch, Large time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models, Monatsh. Math. 154, 39-50 (2008) - Published version
41. J. A. Carrillo, M. Di Francesco, and C. Lattanzio, Contractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws, Bollettino U.M.I. (8) 10-B, 277-292 (2007) - Published version
42. M. Di Francesco, Initial value problem and relaxation limits of the Hamer model for radiating gases in several space variables, NoDEA Nonlinear Differential Equations Appl. 13, no. 5-6, 531-562 (2007) - Published version
43. J. A. Carrillo, M. Di Francesco, and M. P. Gualdani, Semidiscretization and long-time asymptotics of nonlinear diffusion equations, Commun. Math. Sci. 5, 21-53 (2007) - Published version
44. J. A. Carrillo, M. Di Francesco, and G. Toscani, Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering, Proc. Amer. Math. Soc. 135, 353-363 (2007) - Published version
45. J. A. Carrillo, M. Di Francesco, and C. Lattanzio, Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws, Journal of Differential Equations, 231 (2), 425-458 (2006) - Published version
46. M. Burger, M. Di Francesco, and Y. Dolak-Struss, The Keller-Segel model for chemotaxis with prevention of overcrowding: linear vs. nonlinear diffusion, SIAM J. Math. Anal. 38, 1288-1315 (2006) - Published version
47. M. Di Francesco and C. Lattanzio, Optimal L1 decay rates to diffusion waves for the Hamer model of radiating gases, Appl. Math. Lett. 19, no. 10, 1046-1052 (2006) - Published version
48. J. A. Carrillo, M. Di Francesco, and G. Toscani, Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for nonlinear diffusions, Archive for Rational Mechanics and Analysis, 180 (1), 127-149 (2006) - Published version
49. M. Di Francesco and C. Lattanzio, Diffusive relaxation 3x3 model for a system of viscoelasticity, Asymptotic Analysis, IOS Press, 40 (3,4), 235-253 (2004) - Published version
50. M. Di Francesco and P. A. Markowich, Entropy dissipation and Wasserstein metric methods for the Viscous Burgers' equation: convergence to diffusive waves, Partial differential equations and inverse problems, 145-165, Contemp. Math., 362, Amer. Math. Soc., Providence, RI, (2004) - Published version
51. M. Di Francesco and P. Marcati, Singular convergence to nonlinear diffusion waves for solutions to the Cauchy problem for the Compressible Euler equations with damping, Mathematical Models and Methods in Applied Sciences. Vol. 12, n. 9, 1317-1336 (2002) - Published version