18 citations · 43 across the 16 of their papers we have counts for
20 papers
Fully discrete follow-the-leader approximation of one-dimensional scalar conservation laws with vacuum
M. Di Francesco, S. Fagioli, V. Iorio +1
We present a fully discrete particle approximation for one-dimensional scalar conservation laws. Under suitable monotonicity assumptions on the macroscopic velocity, we construct a…
Measure solutions, smoothing effect, and deterministic particle approximation for a conservation law with nonlocal flux
M. Di Francesco, S. Fagioli, E. Radici
We consider a class of nonlocal conservation laws with an interaction kernel supported on the negative real half-line and featuring a decreasing jump at the origin. We provide, for…
Opinion formation on evolving network. The DPA method applied to a nonlocal cross-diffusion PDE-ODE system
Simone Fagioli, Gianluca Favre
We study a system of nonlocal aggregation cross-diffusion PDEs that describe the evolution of opinion densities on a network. The PDEs are coupled with a system of ODEs that descri…
The mathematical theory of Hughes' model: a survey of results
Debora Amadori, Boris Andreianov, Marco Di Francesco +9
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version…
Second order two-species systems with nonlocal interactions: existence and large damping limits
Marco Di Francesco, Simone Fagioli, Valeria Iorio
We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to ext…
Optimal control problems of nonlocal interaction equations
S. Fagioli, A. Kaufmann, E. Radici
In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be inf…
Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts
Luca Alasio, Maria Bruna, Simone Fagioli +1
We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate-parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interac…
On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility
Simone Fagioli, Oliver Tse
We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the…
Opinion Formation Systems via Deterministic Particles Approximation
Simone Fagioli, Emanuela Radici
We propose an ODE-based derivation for a generalized class of opinion formation models either for single and multiple species (followers, leaders, trolls). The approach is purely d…
Multiple Patterns Formation for an Aggregation/Diffusion Predator-Prey System
S. Fagioli, Y. Jaafra
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is des…
Deterministic particle approximation for nonlocal transport equations with nonlinear mobility
M. Di Francesco, S. Fagioli, E. Radici
We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sc…
Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation
Simone Fagioli, Emanuela Radici
We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal versio…
Nonlinear degenerate cross-diffusion systems with nonlocal interaction
M. Di Francesco, A. Esposito, S. Fagioli
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sc…
Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization
Luigi C. Berselli, Simone Fagioli, Stefano Spirito
We prove that weak solutions obtained as limits of certain numerical space-time discretizations are suitable in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. More precisely,…
Sorting Phenomena in a Mathematical Model For Two Mutually Attracting/Repelling Species
Martin Burger, Marco Di Francesco, Simone Fagioli +1
Macroscopic models for systems involving diffusion, short-range repulsion, and long-range attraction have been studied extensively in the last decades. In this paper we extend the…
A deterministic particle approximation for non-linear conservation laws
Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini +1
We review our analytical and numerical results obtained on the microscopic Follow-The-Leader (FTL) many particle approximation of one-dimensional conservation laws. More precisely,…
Follow-the-leader approximations of macroscopic models for vehicular and pedestrian flows
Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini +1
We review recent results and present new ones on a deterministic follow-the-leader particle approximation of first and second order models for traffic flow and pedestrian movements…
Deterministic particle approximation of scalar conservation laws
Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini
In this paper we prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously o…
Deterministic particle approximation of the Hughes model in one space dimension
M. Di Francesco, S. Fagioli, M. D. Rosini +1
In this paper we present a new approach to the solution to a generalized version of Hughes' models for pedestrian movements based on a follow-the-leader many particle approximation…
Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic
M. Di Francesco, S. Fagioli, M. D. Rosini
We consider the Follow-The-Leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi-population formulation. We prove rigorous convergence to weak solutio…