6 papers
Optimal control of a kinetic model describing social interactions on a graph
Jonathan Franceschi, Nadia Loy
In this paper we introduce the optimal control of a kinetic model describing agents who migrate on a graph and interact within its nodes exchanging a physical quantity. As a protot…
Phenotype-structuring of non-local kinetic models of cell migration driven by environmental sensing
Tommaso Lorenzi, Nadia Loy, Chiara Villa
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migrati…
The Bennati-Dragulescu-Yakovenko model in the continuous setting: PDE derivation and long-time behavior
Fei Cao, Nadia Loy
In this manuscript, we develop and analyze a continuous version of the well-known Bennati-Dragulescu-Yakovenko (BDY) dollar-exchange discrete model. Starting from the conservative…
A novel linear transport model with distinct scattering mechanisms for direction and speed
Martina Conte, Nadia Loy
We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affect…
Linear inelastic kinetic equations modelling the spread of fake news and its interplay with personal awareness
Martina Fraia, Nadia Loy, Andrea Tosin
In this paper, we introduce a kinetic model which describes a learning process leading individuals to build personal awareness about fake news. Next, we embed the results of this m…
Essentials of the kinetic theory of multi-agent systems
Nadia Loy, Andrea Tosin
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have esta…