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Publications:

Preprints:

  1. M. Di Francesco, V. Iorio, 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
  2. 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 - Submitted preprint - PDF on arXiv.org

Published or forthcoming papers:

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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.
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. M. Di Francesco, and S. Fagioli, Measure solutions for nonlocal interaction PDEs with two species - Nonlinearity 26, 2777-2808 (2013) - Published version
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. M. Di Francesco and J. Rosado, Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding, Nonlinearity 21, 2715–2730 (2008) - Published version
  38. 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
  39. 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
  40. 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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
  48. 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
  49. 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
  50. 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

My collaborators at UnivAq:

Current collaborators
Former collaborators

Past research grants:

  • In 2018 I held a FFABR research fund awarded by the Italian Ministery of Education and Research (MIUR).
  • In 2017 I held a research fund awarded by the University of L'Aquila as a reward for an unsuccessful ERC proposal with score range 30-39%. The project title is "DP-LAND: Deterministic Particles for Local And Nonlocal Dynamics".
  • 2012-2014: Marie Curie CIG Grant Ref. 321957 "DifNonLoc - Diffusive Partial Differential Equations with Nonlocal Interaction in Biology and Social Sciences".
  • 2011-2012: Ramon y Cajal grant: "Partial Differential Equations in Biology, Medicine and Social Sciences". Ref. RYC-2010-06412.
  • 2012: ESF (European Science Foundation) grant for the organization of an ESF Research Conference. Title: "Applied Partial Differential Equations in Physics, Biology and Social Sciences: classical and modern perspectives"
  • 2010: GNAMPA (Italian group of Analysis, Probability, and Applications) mini project "Equazioni di trasporto applicate alla fisica, alla biologia e alle scienze sociali".

My research activity in short:

My research activity is focused on the analysis of partial differential equations and systems of equations, with main focus on

  • Equations with nonlocal interactions and nonlinear diffusion (aggregation-diffusion)
  • Vehicular and pedestrian traffic flow models of continuum conservation-law type
  • Deterministic particle approximation of transport-diffusion PDEs
  • Optimal transport formulation of evolutionary PDEs
  • Nonlinear equations and systems with cross diffusion and reaction
  • Biomathematics, with special focus on chemotaxis modelling
  • Diffusive relaxation phenomena

Here is my PhD Thesis, which I defended in 2004.

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