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We consider a kinetic model describing some mechanisms of opinion formation in the framework of referendums, where the individuals, who can interact between themselves and modify their opinion by means of spontaneous self-thinking, are moreover under the influence of mass media. We study, at the numerical level, both the transient and the asymptotic regimes. In particular, we point out that a plurality of media, with different orientations, is a key ingredient to allow pluralism and prevent consensus. The forecasts of the model are compared to some surveys related to the Scottish independence referendum of 2014. [ABSTRACT FROM AUTHOR]

We consider the non-reactive elastic Boltzmann equation for multicomponent gaseous mixtures. We deduce, under the standard diffusive scaling, that well prepared initial conditions lead to solutions satisfying the Maxwell-Stefan diffusion equations in the vanishing Mach and Knudsen numbers limit. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we use a kinetic description to study the effect of different psychologies on the evolution of the opinion with respect to a binary choice, in a closed group. We show that the interaction between individuals with different reactions regarding the exchange of opinion induces certain phenomena, such as the concentration of opinions or the cyclic-in-time behaviour of the distribution function. We provide an existence and uniqueness result for the model, and numerically test it in some relevant cases. [Copyright &y& Elsevier]

We consider a mixture of N ideal, polytropic gases. Each species is described by a distribution function f i(t, x, v, I) ≥ 0, 1 ≤ i ≤ N, defined on ${\rm I\!R}_+\times{\rm I\!R}^3\times{\rm I\!R}^3\times{\rm I\!R}_+$, and its evolution is governed by a Boltzmann-type equation. In order to recover the energy law of polytropic gases, the authors of [4] proposed a kinetic model in the framework of a weighted L1 space. Another approach has been developed in [3] in the context of polyatomic gases. Following this previous lead, our model provides a L2 framework in both variables v and I, to eventually perform a mathematical study of the diffusion asymptotics, as it was done in [2] for a model without energy exchange. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]