Research

I am interested in applied mathematical analysis, focused on partial differential equations, obtained in several applied contexts such as Biology, Medicine and Social Sciences. More precisely:

  • Transport PDE’s with nonlocal interactions with applications to aggregative phenomena in biology and social sciences;
  • Particle methods for conservation laws;
  • Reaction-diffusion equations and systems in biology and medicine;
  • Models in opinion formation and social sciences.

Selected publications:

  1. S. Fagioli, E. Radici: Opinion Formation Systems via Deterministic Particles Approximation. Kinetic and Related Models, 14 (1), 45-76, (2021).

  2. J.A. Carrillo, S. Fagioli, F. Santambrogio, M. Schmidtchen: Splitting schemes & segregation in reaction-(cross-)diffusion systems. SIAM Journal on Mathematical Analysis, 50 (5), 5695–5718, (2018).

  3. M. Burger, M. Di Francesco, S. Fagioli, A. Stevens: Sorting phenomena in a mathematical model for two mutual attracting/repelling species. SIAM Journal on Mathematical Analysis, 50 (3), 3210–3250, (2018).

  4. M. Di Francesco, A. Esposito, S. Fagioli: Nonlinear degenerate cross-diffusion systems with nonlocal interaction. Nonlinear Analysis, 169, (2018), 94-117.

  5. M. Di Francesco, S. Fagioli, M.D. Rosini: Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic. Mathematical Biosciences and Engineering (MBE) 14 (2017), 127-141.

  6. M. Di Francesco, S. Fagioli: Measure solutions for nonlocal interaction PDE's with two species. Nonlinearity 26 (2013), 2777-2808.

Full list of pubblications can be found here

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