Marco Di Francesco

Associate Professor

Coppito 1, Room 1047
marco.difrancesco@univaq.it
0862434712

My research activity is focused on the analysis of partial differential equations and systems of equations. More precisely, I am interested in

  • Equations with nonlocal interactions arising in animal population dynamics
  • Nonlinear diffusion equations
  • Models for the movement of pedestrians, especially of continuum conservation-law type
  • Optimal transport formulation of evolutionary PDEs
  • Nonlinear equations and systems with cross diffusion arising in biological aggregation
  • Reaction-diffusion systems
  • Diffusive models for chemotaxis
  • Diffusive relaxation phenomena
  • Hydrodynamic models in compressible gas-dynamics and semiconductor theory

Preprints:

  1. M. Di Francesco, S. Fagioli, M. D. Rosini, and G. RussoDeterministic particle approximation of the Hughes model in one space dimension - Submitted preprint - PDF
  2. M. Di Francesco, S. Fagioli, and M. D. RosiniMany particle approximation for the Aw-Rascle-Zhang second order model for vehicular traffic - Submitted preprint - PDF

Published or forthcoming articles in refereed journals:

  1. M. Di Francesco and S. FagioliA nonlocal swarm model for predators–prey interactions - Mathematical Models and Methods in Applied Sciences, 26 (319), 319-355 (2016)
  2. M. Di Francesco and M. D. RosiniRigorous 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)
  3. M. Di Francesco, M. Fornasier, J.-C. Hütter, and D. MatthesAsymptotic 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)
  4. G. A. Bonaschi, J. A. Carrillo, M. Di Francesco, and M. A. PeletierEquivalence 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)
  5. J. A. Carrillo, M. Di Francesco, and G. ToscaniCondensation phenomena in nonlinear drift equations- To appear on Ann. Sc. Norm. Super. Pisa Cl. Sci.
  6. M. Burger, M. Di Francesco, P. A. Markowich, and M.-T. WolframMean field games with nonlinear mobilities in pedestrian dynamics - Discrete and Continuous Dynamical Systems - B, 19 (2014) 1311 - 1333
  7. M. Di Francesco, and D. MatthesCurves of steepest descent are entropy solutions for a class of degenerate convection-diffusion equations - Calc. Var. PDEs - 50 (2014), no. 1-2, 199–230.
  8. M. Di Francesco, and S. FagioliMeasure solutions for nonlocal interaction PDEs with two species - Nonlinearity 26 (2013), 2777-2808
  9. M. Burger, M. Di Francesco, and M. FranekStationary states of quadratic diffusion equations with long-range attraction - Commun. Math. Sci. 11 (2013), no. 3, 709–738.
  10. D. Amadori, and M. Di FrancescoThe one-dimensional Hughes model for pedestrian flow: Riemann--type solutions - Acta Mathematica Scientia 32 (1) (2012), 259-280
  11. J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, and D. SlepcevConfinement in nonlocal interaction equations - Nonlinear Analysis 75, 550–558 (2012)
  12. J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, and D. SlepcevGlobal-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations - Duke Mathematical Journal, 156 (2), 229-271 (2011)
  13. M. Di Francesco, P. A. Markowich, J.-F. Pietschmann, and M.-T. WolframOn the Hughes' model for pedestrian flow: The one-dimensional case - Journal of Differential Equations, 250 (3), 1334-1362 (2011)
  14. M. Burger, M. Di Francesco, J.-F. Pietschmann, and B. SchlakeNonlinear Cross-Diffusion with Size Exclusion - SIAM J. Math. Anal. 42 (6), 2842-2871 (2010)
  15. M. Di Francesco, A. Lorz, and P. A. MarkowichChemotaxis 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)
  16. M. Di Francesco and M. TwarogowskaAsymptotic 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)
  17. M. Di Francesco and D. DonatelliSingular convergence of nonlinear hyperbolic chemotaxis systems to Keller-Segel type models, Discrete and Continuous Dynamical Systems (B), 13 (1), 79-100 (2010)
  18. M. Di Francesco and J. RosadoFully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding, Nonlinearity 21, 2715–2730 (2008)
  19. M. Di Francesco, K. Fellner, and P. A. MarkowichThe entropy dissipation method for spatially inhomogeneous reaction-diffusion type systems, Proc. R. Soc. A 464, 3273-3300 (2008)
  20. M. Burger and M. Di FrancescoLarge time behavior of nonlocal aggregation models with nonlinear diffusion, Networks and Heterogeneous Media, 3 (4), 749-785 (2008)
  21. M. Di Francesco, K. Fellner, and H. LiuA non-local conservation law with nonlinear "radiation" inhomogeneity, J. Hyperbolic Differ. Equ. 5, no. 1, 1-23 (2008)
  22. M. Di Francesco, and M. WunschLarge time behavior in Wasserstein spaces and relative entropy for bipolar drift-diffusion-Poisson models, Monatsh. Math. 154, 39-50 (2008)
  23. M. Di FrancescoInitial 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)
  24. J. A. Carrillo, M. Di Francesco, and G. ToscaniStrict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering, Proc. Amer. Math. Soc. 135, 353-363 (2007)
  25. J. A. Carrillo, M. Di Francesco, and M. P. GualdaniSemidiscretization and long-time asymptotics of nonlinear diffusion equations, Commun. Math. Sci. 5, 21-53 (2007)
  26. M. Burger, M. Di Francesco, and Y. Dolak-StrussThe Keller-Segel model for chemotaxis with prevention of overcrowding: linear vs. nonlinear diffusion, SIAM J. Math. Anal. 38, 1288-1315 (2006).
  27. J. A. Carrillo, M. Di Francesco, and C. LattanzioContractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws, Journal of Differential Equations, 231 (2), 425-458 (2006)
  28. M. Di Francesco and C. LattanzioOptimal L1 decay rates to diffusion waves for the Hamer model of radiating gases, Appl. Math. Lett. 19, no. 10, 1046-1052 (2006)
  29. J. A. Carrillo, M. Di Francesco, and G. ToscaniIntermediate asymptotics beyond homogeneity and self-similarity: long time behavior for nonlinear diffusions, Archive for Rational Mechanics and Analysis, 180 (1), 127-149 (2006)
  30. M. Di Francesco and C. LattanzioDiffusive relaxation 3x3 model for a system of viscoelasticity, Asymptotic Analysis, IOS Press, 40 (3,4), 235-253 (2004)
  31. M. Di Francesco and P. MarcatiSingular 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)

Conference proceedings and review papers:

  1. M. Di Francesco, (Review paper) Scalar conservation laws seen as gradient flows: known results and new perspectives - Submitted preprint - PDF
  2. M. Burger, M. Di Francesco, P. A. Markowich, and M.-T. WolframOn 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)
  3. J. A. Carrillo, M. Di Francesco, and C. LattanzioContractivity and asymptotics in Wasserstein metrics for viscous nonlinear scalar conservation laws, Bollettino U.M.I. (8) 10-B, 277-292 (2007)
  4. M. Di Francesco and P. A. MarkowichEntropy 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)