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, A. Kaufmann, E. Radici: Optimal control problems of nonlocal interaction equations. ESAIM: COCV, 29, 40 (2023).

2. S. Fagioli, O. Tse: On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility. Nonlinear Analysis, 221, 112904, (2022).

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

4. 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).

5. 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).

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

7. 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.

8. 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