- M. Di Francesco and G. Stivaletta, Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux. - Submitted preprint - PDF
- 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. - Submittted preprint - PDF
Published or forthcoming papers:
- M. Di Francesco, S. Fagioli, and E. Radici, Deterministic particle approximation for nonlocal transport equations with nonlinear mobility - To appear on Journal of Differential equations (available online) - PDF
- M. Di Francesco and Y. Jaafra, Multiple large-time behavior of nonlocal interaction equations with quadratic diffusion - To appear on Kinetic and Related Models - PDF
- 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) - PDF
- M. Di Francesco, A. Esposito, and S. Fagioli, Nonlinear degenerate cross-diffusion systems with nonlocal interaction - Nonlinear Analysis, Volume 169, 94-117 (2018) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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) - PDF
- 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)
- M. Di Francesco, and S. Fagioli, Measure solutions for nonlocal interaction PDEs with two species - Nonlinearity 26, 2777-2808 (2013) - PDF
- 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) - PDF
- 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) - PDF
- J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, and D. Slepcev, Confinement in nonlocal interaction equations - Nonlinear Analysis 75, 550–558 (2012) - PDF
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- M. Di Francesco and J. Rosado, Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding, Nonlinearity 21, 2715–2730 (2008)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
My research group:
- Since January 2018 I hold a FFABR research fund awarded by the Italian Ministery of Education and Research (MIUR).
- Since June 2017 I hold 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".
- My research activity is partially supported by the MathMods programme.
Past research grants:
- 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.