
Publications:
Preprints:
 M. Di Francesco and G. Stivaletta, The onesided Lipschitz condition in the followtheleader approximation of scalar conservation laws.  Submitted preprint  PDF
Published or forthcoming papers:
 M. Di Francesco, A. Esposito, and M. Schmidtchen, Manyparticle limit for a system of interaction equations driven by Newtonian potentials.  To appear on Calculus of Variations and Partial Differential Equations  PDF
 M. Di Francesco and G. Stivaletta, Convergence of the followtheleader scheme for scalar conservation laws with space dependent flux.  Discrete and Continuous Dynamical Systems 40 (1), 233266 (2020)  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.  Discrete and Continuous Dynamical Systems 40 (2), 11911231 (2020)  PDF
 M. Di Francesco, S. Fagioli, and E. Radici, Deterministic particle approximation for nonlocal transport equations with nonlinear mobility  Journal of Differential Equations, 266 (5), 28302868 (2019)  PDF
 M. Di Francesco and Y. Jaafra, Multiple largetime behavior of nonlocal interaction equations with quadratic diffusion  Kinetic and Related Models 12 (2), 303322 (2019)  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 crossdiffusion systems with nonlocal interaction  Nonlinear Analysis, Volume 169, 94117 (2018)  PDF
 M. Di Francesco, S. Fagioli, M.D. Rosini, and G.Russo, A deterministic particle approximation for nonlinear 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).
 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, Followtheleader 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 333378 (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), 215237 (2017)  PDF
 M. Di Francesco, S. Fagioli, and M. D. Rosini, Many particle approximation for the AwRascleZhang second order model for vehicular traffic  Mathematical Biosciences and Engineering, 14 (1), 127141 (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, 145171 (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), 319355 (2016)  PDF
 M. Di Francesco and M. D. Rosini, Rigorous derivation of nonlinear scalar conservation laws from followtheleader type models via many particle limit  Archive for rational mechanics and analysis, 217 (3), 831871 (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), 414441 (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 convectiondiffusion equations  Calc. Var. PDEs  50, no. 12, 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, 31283133 (2013)
 M. Di Francesco, and S. Fagioli, Measure solutions for nonlocal interaction PDEs with two species  Nonlinearity 26, 27772808 (2013)  PDF
 M. Burger, M. Di Francesco, and M. Franek, Stationary states of quadratic diffusion equations with longrange attraction  Commun. Math. Sci. 11, no. 3, 709–738 (2013)  PDF
 D. Amadori, and M. Di Francesco, The onedimensional Hughes model for pedestrian flow: Riemanntype solutions  Acta Mathematica Scientia 32 (1), 259280 (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 reactiondiffusion system arising in cancer modelling  Mathematical and Computer modelling, 53 (78), 14571468 (2011)
 J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, and D. Slepcev, Globalintime weak measure solutions and finitetime aggregation for nonlocal interaction equations  Duke Mathematical Journal, 156 (2), 229271 (2011)
 M. Di Francesco, P. A. Markowich, J.F. Pietschmann, and M.T. Wolfram, On the Hughes' model for pedestrian flow: The onedimensional case  Journal of Differential Equations, 250 (3), 13341362 (2011)
 M. Burger, M. Di Francesco, J.F. Pietschmann, and B. Schlake, Nonlinear CrossDiffusion with Size Exclusion  SIAM J. Math. Anal. 42 (6), 28422871 (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), 14371453 (2010)
 M. Di Francesco and D. Donatelli, Singular convergence of nonlinear hyperbolic chemotaxis systems to KellerSegel type models, Discrete and Continuous Dynamical Systems (B), 13 (1), 79100 (2010)
 M. Burger and M. Di Francesco, Large time behavior of nonlocal aggregation models with nonlinear diffusion, Networks and Heterogeneous Media, 3 (4), 749785 (2008)
 M. Di Francesco, K. Fellner, and P. A. Markowich, The entropy dissipation method for spatially inhomogeneous reactiondiffusion type systems, Proc. R. Soc. A 464, 32733300 (2008)
 M. Di Francesco and J. Rosado, Fully parabolic KellerSegel model for chemotaxis with prevention of overcrowding, Nonlinearity 21, 2715–2730 (2008)
 M. Di Francesco, K. Fellner, and H. Liu, A nonlocal conservation law with nonlinear "radiation" inhomogeneity, J. Hyperbolic Differ. Equ. 5, no. 1, 123 (2008)
 M. Di Francesco, and M. Wunsch, Large time behavior in Wasserstein spaces and relative entropy for bipolar driftdiffusionPoisson models, Monatsh. Math. 154, 3950 (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) 10B, 277292 (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. 56, 531562 (2007)
 J. A. Carrillo, M. Di Francesco, and M. P. Gualdani, Semidiscretization and longtime asymptotics of nonlinear diffusion equations, Commun. Math. Sci. 5, 2153 (2007)
 J. A. Carrillo, M. Di Francesco, and G. Toscani, Strict contractivity of the 2Wasserstein distance for the porous medium equation by masscentering, Proc. Amer. Math. Soc. 135, 353363 (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), 425458 (2006)
 M. Burger, M. Di Francesco, and Y. DolakStruss, The KellerSegel model for chemotaxis with prevention of overcrowding: linear vs. nonlinear diffusion, SIAM J. Math. Anal. 38, 12881315 (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, 10461052 (2006)
 J. A. Carrillo, M. Di Francesco, and G. Toscani, Intermediate asymptotics beyond homogeneity and selfsimilarity: long time behavior for nonlinear diffusions, Archive for Rational Mechanics and Analysis, 180 (1), 127149 (2006)
 M. Di Francesco and C. Lattanzio, Diffusive relaxation 3x3 model for a system of viscoelasticity, Asymptotic Analysis, IOS Press, 40 (3,4), 235253 (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, 145165, 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, 13171336 (2002)

My research group:
Current members
Former members
Research projects:
 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 3039%. The project title is "DPLAND: Deterministic Particles for Local And Nonlocal Dynamics".
 My research activity is partially supported by the MathMods programme.
Past research grants:
 20122014: Marie Curie CIG Grant Ref. 321957 "DifNonLoc  Diffusive Partial Differential Equations with Nonlocal Interaction in Biology and Social Sciences".
 20112012: Ramon y Cajal grant: "Partial Differential Equations in Biology, Medicine and Social Sciences". Ref. RYC201006412.
 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 (aggregationdiffusion)
 Vehicular and pedestrian traffic flow models of continuum conservationlaw type
 Deterministic particle approximation of transportdiffusion 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.

