Francesco Salvarani

@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 = {2022-01-01},

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{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{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{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 = {2020-01-01},

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{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 = {2020-01-01},

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{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 = {2018-01-01},

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}

}