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.
Emanuela Radici
Preprints:
F.A. Chiarello, S. Fagioli, M.D. Rosini: Existence result for a 2 x 2 system of conservation laws with discontinuous flux and applications. Submitted preprint, (2024)
Publications:
Y.-P. Choi, S. Fagioli, V. Iorio: Small inertia limit for coupled kinetic swarming models. Journal of Nonlinear Science, 35, 39 (2025) Preprint
M. Di Francesco, S. Fagioli, E. Radici: Measure solutions, smoothing effect, and deterministic particle approximation for a conservation law with nonlocal flux. To appear on Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Preprint, (2025)
S. Fagioli, E. Radici, L. Romagnoli: On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis. Partial Differential Equations and Applications, 6, 3, (2025). Preprint
S. Fagioli, G. Favre: Opinion formation on evolving network. The DPA method applied to a nonlocal cross-diffusion PDE-ODE system. European Journal of Applied Mathematics, 35, 6, 748-775, (2024) Preprint.
S. Fagioli, A. Kaufmann, E. Radici: Optimal control problems of nonlocal interaction equations. ESAIM: COCV, 29, 40, (2023). Preprint.
M. Di Francesco, S. Fagioli, V. Iorio: Second order two-species systems with nonlocal interactions: existence and large damping limits. Acta Applicandae Mathematicae, 184, 9, (2023). Preprint.
L. Alasio, M. Bruna, S. Fagioli, S. Schulz: Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts. Nonlinear Analysis, 223, 113064, (2022). Preprint.
S. Fagioli, O. Tse: On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility. Nonlinear Analysis, 221, 112904, (2022). Preprint.
S. Fagioli, Y. Jaafra: Multiple patterns formation for an aggregation/diffusion predator-prey system. Networks & Heterogeneous Media, 16(3), 377 - 411, (2021). Preprint.
S. Fagioli, E. Radici: Opinion Formation Systems via Deterministic Particles Approximation. Kinetic and Related Models, 14 (1), 45-76, (2021). Preprint.
N. Ansini, S. Fagioli: Nonlinear diffusion equations with degenerate fast-decay mobility by coordinate transformation. Communications in Mathematical Sciences, 18 (2), 459 – 486, (2020). Preprint.
J.A. Carrillo, M. Di Francesco, A. Esposito, S. Fagioli, M. Schmidtchen: Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions. Discrete and Continuous Dynamical Systems- Series A, 40(2), pp. 1191-1231, (2020). Preprint.
M. Di Francesco, S. Fagioli, E. Radici: Deterministic particle approximation for nonlocal transport equations with nonlinear mobility. Journal of Differential Equations, 266(5), 2830-2868, (2019). Preprint
L.C. Berselli, S. Fagioli, S. Spirito: Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization. Journal des Mathématiques Pures et Appliquées, 125, 189-2018, (2019). Preprint.
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). Preprint.
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). Preprint.
S. Fagioli, E. Radici: Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation. Math. Models Methods Appl. Sci., 28, (9), 1801-1829, (2018). Preprint.
M. Di Francesco, A. Esposito, S. Fagioli: Nonlinear degenerate cross-diffusion systems with nonlocal interaction. Nonlinear Analysis, 169, 94-117, (2018). Preprint.
M. Di Francesco, S. Fagioli, M.D. Rosini: Deterministic particle approximation of scalar conservation laws. Boll. Unione Mat. Ital. 10, 215 - 237, (2017). Preprint.
M. Di Francesco, S. Fagioli, M.D. Rosini, G. Russo: Deterministic particle approximation of the Hughes model in one space dimension. Kinetic and Related Models (KRM) 10, 215 - 237, (2017). Preprint.
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, 127-141, (2017). Preprint.
M. Di Francesco, S. Fagioli: A nonlocal swarm model for predators–prey interactions. Math. Models Methods Appl. Sci. 26, 319, (2016). Preprint.
M. Di Francesco, S. Fagioli: Measure solutions for nonlocal interaction PDE's with two species. Nonlinearity, 26, 2777-2808, (2013). Preprint.
Book chapters:
D. Amadori, B. Andreianov, M. Di Francesco, S. Fagioli, T. Girard, P. Goatin, P. Markowich, J.-F. Pietschmann, M.D. Rosini, G. Russo, G. Stivaletta and M.T. Wolfram: The mathematical theory of Hughes' model: a survey of results, In: Bellomo, N., Gibelli, L. (eds) Crowd Dynamics, Volume 4. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. (2023) Preprint.
M. Di Francesco, S. Fagioli, M.D. Rosini, G. Russo: Follow-the-Leader approximations of macroscopic models for vehicular and pedestrian flows. Active particles, Vol 1. (Bellomo, N., Degond, P. and Tadmor, E. Eds.), Birkhäuser Basel, 333-378, (2017). Preprint.
Conference papers:
S. Fagioli, A. Festa, C. Lattanzio, M. Bellotti, G. Cutrupi, C. Criminisi, G. Muratore, D. Micheli, A. Vannelli: On the Validity of the LWR Model. TRB 2021 Annual Meeting, 2021.
M. Di Francesco, S. Fagioli, M.D. Rosini, G.Russo: A deterministic particle approximation for non-linear 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.