Francesco Salvarani

@article{bongini_2948,

title = {MEAN FIELD GAMES OF CONTROLS WITH DIRICHLET BOUNDARY CONDITIONS},

author = {Mattia Bongini and Francesco Salvarani},

url = {https://www.esaim-cocv.org/articles/cocv/abs/2024/01/cocv230134/cocv230134.html},

year  = {2024},

date = {2024-04-01},

journal = {Esaim-Control Optimisation And Calculus Of Variations},

volume = {30},

pages = {32},

abstract = {In this paper, we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a mean-field game of controls setting, that is in which the dynamics of each agent is affected not only by the average position of the rest of the agents but also by their average optimal choice. This setting allows the modeling of more realistic real-life scenarios in which agents not only will leave the domain at a certain point in time (like during the evacuation of pedestrians or in debt refinancing dynamics) but also act competitively to anticipate the strategies of the other agents. We shall establish the existence of Nash Equilibria for such class of mean-field game of controls systems under certain regularity assumptions on the dynamics and the Lagrangian cost. Much of the paper is devoted to establishing several a priori estimates which are needed to circumvent the fact that the mass is not conserved (as we are in a Dirichlet boundary condition setting). In the conclusive sections, we provide examples of systems falling into our framework as well as numerical implementations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{bernard_2401,

title = {On the Homogenization of the Renewal Equation with Heterogeneous External Constraints},

author = {Etienne Bernard and Francesco Salvarani},

url = {https://link.springer.com/article/10.1007/s10440-023-00594-2},

year  = {2023},

date = {2023-10-01},

journal = {Acta Applicandae Mathematicae},

volume = {187},

number = {1},

pages = {4},

abstract = {We study the homogenization limit of the renewal equation with heterogeneous external con- straints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{salvarani_2286,

title = {Homogenization of the linear Boltzmann equation with a highly oscillating scattering term in extended phase space},

author = {Francesco Salvarani and Etienne Bernard},

url = {https://doi.org/10.1016/j.aml.2023.108672},

year  = {2023},

date = {2023-09-01},

journal = {Applied Mathematics Letters},

volume = {143},

pages = {108672},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{charles_2316,

title = {Mathematical and numerical study of a kinetic model describing the evolution of planetary rings},

author = {Frédérique Charles and Annamaria Massimini and Francesco Salvarani},

url = {https://www.sciencedirect.com/science/article/pii/S0898122123001724},

year  = {2023},

date = {2023-08-01},

journal = {Computers & Mathematics With Applications},

volume = {143},

number = {1},

pages = {48-56},

abstract = {In this paper, we study a kinetic model describing the evolution of planetary dust under the action of a planet and its satellites. In particular, we focus our attention on the formation of planetary rings and the role of shepherd moons. The equation describing the considered physical phenomenon is of Vlasov type, posed in an evolutionary domain in time. We first study some theoretical properties of the model. Then, we describe a numerical method, suitable for the study of kinetic equations in evolutionary domains with possibly complicated geometries. Finally, we show and comment some simulations. In particular, our numerical simulations show that shepherd moons play a key role in the formation and maintenance of divisions between rings.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{borsoni_1875,

title = {Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions},

author = {Thomas Borsoni and Laurent Boudin and Francesco Salvarani},

url = {https://www.sciencedirect.com/science/article/pii/S0022247X22005935?via%3Dihub},

year  = {2023},

date = {2023-01-01},

journal = {Journal Of Mathematical Analysis And Applications},

volume = {517},

number = {1},

pages = {126579},

abstract = {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 peculiar structure of resonant collision rules allows to tensorize the problem into a velocity-related one, neighbouring the monatomic case, and an internal energy-related one. Our analysis is based on a specific treatment of the internal energy contributions. We also propose a geometric variant of Grad's proof of the same compactness property in the monatomic case.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{boudin_1894,

title = {A kinetic model of polyatomic gas with resonant collisions},

author = {Laurent Boudin and Alex Rossi and Francesco Salvarani},

url = {https://doi.org/10.1007/s11587-022-00733-1},

year  = {2022},

date = {2022-09-01},

journal = {Ricerche Di Matematica},

keywords = {},

pubstate = {online},

tppubtype = {article}

}

@article{boudin_1819,

title = {Exponential Convergence Towards Consensus for Non-Symmetric Linear First-Order Systems in Finite and Infinite Dimensions},

author = {Laurent Boudin and Francesco Salvarani and Emmanuel Trélat},

url = {https://epubs.siam.org/doi/abs/10.1137/21M1416102},

year  = {2022},

date = {2022-05-01},

journal = {Siam Journal On Mathematical Analysis},

volume = {54},

number = {3},

pages = {2727-2752},

abstract = {We consider finite and infinite-dimensional first-order consensus systems with time- constant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function. We investigate here the convergence to consensus in the non-symmetric case: we identify a positive weight which allows us to define a weighted mean corresponding to the consensus and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{braghini_1820,

title = {Effects of Hidden Opinion Manipulation in Microblogging Platforms},

author = {Giulia Braghini and Francesco Salvarani},

url = {https://www.worldscientific.com/doi/abs/10.1142/S0219525921500090},

year  = {2021},

date = {2021-11-01},

journal = {Advances In Complex Systems},

volume = {24},

number = {5},

pages = {2150009},

abstract = {This paper studies a model for describing opinions' evolution in a community linked by microblogging directed network systems. The network can evolve in time by means of the creation and the deletion of some connections. When a connexion is created, the individuals have access to the whole history of posts written by the corresponding author and, when a connexion is destroyed, all the posts written by the corresponding author become invisible. The agents' opinions are described by a set of continuous opinion variables in the closed interval  Omega=[-1,1]. They represent the agreement (or disagreement) of the corresponding agent with respect to a binary question (such as a referendum or an election with two candidates). The model takes into account the effects on public opinion caused by the sign and the intensity of the initial opinions of the agents, their activity in microblogging platforms the presence of leaders and the possible manipulations of the visibility of the posts by the microblogging platform owner. The model is written as a system of integro-differential equations and simulated by using a Runge-Kutta method. We show that hidden manipulation can have an important impact on the public opinion formation and that very mild interventions of the network owner may induce major effects on the population. In our simulations, the effect of hidden manipulation is shown to be more efficient in driving the public opinion than the action of a leader, in the case of bounded confidence models and for short-time intervals.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{pouradier_duteil_1268,

title = {Kinetic approach to the collective dynamics of the rock paper scissors binary game},

author = {Nastassia Pouradier Duteil and Francesco Salvarani},

url = {https://www.sciencedirect.com/science/article/pii/S0096300320304549#!},

year  = {2021},

date = {2021-01-01},

journal = {Applied Mathematics And Computation},

volume = {388},

pages = {125496},

abstract = {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 we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{bernard_1413,

title = {Optimal Estimate of the Spectral Gap for the Degenerate Goldstein-Taylor Model},

author = {Etienne Bernard and Francesco Salvarani},

url = {https://link.springer.com/article/10.1007/s10955-020-02631-y},

year  = {2020},

date = {2020-11-01},

journal = {Journal Of Statistical Physics},

volume = {181},

pages = {1470-1471},

abstract = {x},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{charles_1518,

title = {Mathematical and numerical study of a dusty Knudsen gas mixture},

author = {Frédérique Charles and Francesco Salvarani},

url = {https://link.springer.com/article/10.1007/s10440-019-00277-x},

year  = {2020},

date = {2020-08-01},

journal = {Acta Applicandae Mathematicae},

volume = {168},

number = {1},

pages = {17-31},

abstract = {We consider a mixture composed of a gas and dust particles in a very rarefied setting. Whereas the dust particles are individually described, the surrounding gas is treated as a Knudsen gas, in such a way that interactions occur only between gas particles and dust by means of diffuse reflection phenomena. After introducing the model, we prove the existence and the uniqueness of the solution and provide a numerical strategy for the study of the equations. At the numerical level, we focus our attention on the phenomenon of energy transfer between the gas and the moving dust particles.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{mula_1514,

title = {Homogenization in the energy variable for a neutron transport model.},

author = {Olga Mula and Francesco Salvarani and Harsha Hutridurga},

url = {https://content.iospress.com/articles/asymptotic-analysis/asy191544},

year  = {2020},

date = {2020-03-01},

journal = {Asymptotic Analysis},

volume = {117},

number = {1-2},

pages = {1-25},

abstract = {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-scale convergence to arrive at the homogenization result. In doing so, we show the induction of a memory effect in the homogenization limit. We also provide some numerical experiments to illustrate our results. In the Appendix, we treat a related case of the harmonic oscillator.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{anwasia_1125,

title = {On the Maxwell- Stefan diffusion limit for reactive mixture of polyatomic gases in non-isothermal setting},

author = {Benjamin Anwasia and Marzia Bisi and Ana Jacinta Soares and Francesco Salvarani},

url = {https://www.aimsciences.org/article/doi/10.3934/krm.2020003},

year  = {2020},

date = {2020-02-01},

journal = {Kinetic And Related Models},

volume = {13},

number = {1},

pages = {63-95},

abstract = {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 the model are derived in the diffusive limit of a kinetic system of Boltzmann equations for the considered mixture, in the general non-isothermal setting. The asymptotic analysis of the kinetic system is performed under a reactive-diffusive scaling for which mechanical collisions are dominant with respect to chemical reactions. The resulting system couples the Maxwell-Stefan equations for the diffusive fluxes with the evolution equations for the number densities of the chemical species and the evolution equation for the temperature of the mixture. The production terms due to the chemical reaction and the Maxwell-Stefan diffusion coefficients are moreover obtained in terms of general collision kernels and parameters of the kinetic model.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{soares_1519,

title = {On the relaxation of the Maxwell-Stefan system to linear diffusion},

author = {Ana Jacinta Soares and Francesco Salvarani},

url = {https://www.sciencedirect.com/science/article/abs/pii/S089396591830154X},

year  = {2018},

date = {2018-11-01},

journal = {Applied Mathematics Letters},

volume = {85},

pages = {15-21},

abstract = {In this note, we rigorously prove the relaxation limit of the Maxwell-Stefan system to a

system of heat equations when all binary diffusion coefficients tend to the same positive value.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}