45 citations · 120 across the 18 of their papers we have counts for
19 papers
Nonlinear oscillations of the amplitude of energetic-particle induced geodesic acoustic modes
E. Sida, A. Biancalani, A. Bottino +2
Energetic particle induced geodesic acoustic modes (EGAMs) are axisymmetric perturbations of the radial electric field in tokamak plasmas. They are driven unstable by the phase spa…
Multiscale analysis of a kinetic equation for mechanotaxis
Benoît Perthame, Francesco Salvarani, Shugo Yasuda
We present a new kinetic equation for cell migration driven by mechanical interactions with the substrate, an effect not previously captured in kinetic models, and essential for ex…
A kinetic model for polyatomic gas with quasi-resonant collisions leading to bi-temperature relaxation processes
Thomas Borsoni, Laurent Boudin, Julien Mathiaud +1
In this article, we extend the Boltzmann framework for polyatomic gases by introducing quasi-resonant kernels, which relax resonant interactions, for which kinetic and internal ene…
A kinetic theory approach to consensus formation in financial markets
Jean-Gabriel Attali, Francesco Salvarani
It is sometimes acknowledged that (sell-side) equity analysts' recommendations influence investors and therefore market prices. In particular, the S&P 500 is expected to decline (r…
Self-similar solutions, regularity and time asymptotics for a nonlinear diffusion equation arising in game theory
Marco Antonio Fontelos, Francesco Salvarani, Nastassia Pouradier Duteil
In this article, we study the long-time asymptotic properties of a non-linear and non-local equation of diffusive type which describes the rock-paper-scissors game in an interconne…
Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions
Thomas Borsoni, Laurent Boudin, Francesco Salvarani
In this paper, we investigate a compactness property of the linearized Boltzmann operator in the context of a polyatomic gas whose molecules undergo resonant collisions. The peculi…
Mean Field Games of Controls with Dirichlet boundary conditions
Mattia Bongini, Francesco Salvarani
In this paper we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a mean-field of control setting, that is in which the dynamics of each…
Exponential convergence towards consensus for non-symmetric linear first-order systems in finite and infinite dimensions
Laurent Boudin, Francesco Salvarani, Emmanuel Trélat
We consider finite and infinite-dimensional first-order consensus systems with timeconstant interaction coefficients. For symmetric coefficients, convergence to consensus is classi…
On a nonlinear parabolic problem arising in the quantum diffusive description of a degenerate fermion gas
Luigi Barletti, Francesco Salvarani
This article studies, both theoretically and numerically, a nonlinear drift-diffusion equation describing a gas of fermions in the zero-temperature limit. The equation is considere…
Kinetic approach to the collective dynamics of the rock-paper-scissors binary game
Nastassia Duteil, Francesco Salvarani
This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently w…
On the Maxwell-Stefan diffusion limit for a reactive mixture of polyatomic gases in non-isothermal setting
Benjamin Anwasia, Marzia Bisi, Francesco Salvarani +1
In this article we deduce a mathematical model of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The equations of th…
Homogenization in the energy variable for a neutron transport model
Harsha Hutridurga, Olga Mula, Francesco Salvarani
This article addresses the homogenization of linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scal…
Existence and uniqueness analysis of a non-isothermal cross-diffusion system of Maxwell-Stefan type
Harsha Hutridurga, Francesco Salvarani
In this article we prove local-in-time existence and uniqueness of solution to a non-isothermal cross-diffusion system with Maxwell-Stefan structure.
Maxwell-Stefan diffusion asymptotic for gas mixtures in non-isothermal setting
Harsha Hutridurga, Francesco Salvarani
A mathematical model is proposed where the classical Maxwell-Stefan diffusion model for gas mixtures is coupled to an advection-type equation for the temperature of the physical sy…
On the Maxwell-Stefan diffusion limit for a mixture of monatomic gases
Harsha Hutridurga, Francesco Salvarani
Multi-species Boltzmann equations for gaseous mixtures, with analytic cross sections and under Grad's angular cutoff assumption, are considered under diffusive scaling. In the limi…
Exponential relaxation to self-similarity for the superquadratic fragmentation equation
Pierre Gabriel, Francesco Salvarani
We consider the self-similar fragmentation equation with a superquadratic fragmentation rate and provide a quantitative estimate of the spectral gap.
The Logit lane assignment model: first results
Nadir Farhi, Habib Haj-Salem, Megan Khoshyaran +4
The Logit lane assignment model has been introduced recently in order to describe multi-lane traffic flow from a macroscopic point of view. The model is based on the idea that each…
Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method
Emmanuel Frénod, Francesco Salvarani, Eric Sonnendrücker
We study the two-scale asymptotics for a charged beam under the action of a rapidly oscillating external electric field. After proving the convergence to the correct asymptotic sta…
The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem
François Golse, Francesco Salvarani
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary condi…