Maxwell-Stefan diffusion asymptotic for gas mixtures in non-isothermal setting

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 system. This coupled system is derived from first principles in the sense that the starting point of our analysis is a system of Boltzmann equations for gaseous mixtures. We perform an asymptotic analysis on the Boltzmann model under diffuse scaling to arrive at the proposed coupled system.Comment: 14 page

Existence and uniqueness analysis of a non-isothermal cross-diffusion system of Maxwell-Stefan type

In this article we prove local-in-time existence and uniqueness of solution to a non-isothermal cross-diffusion system with Maxwell-Stefan structure.Comment: 6 page

Opinion dynamics: kinetic modelling with mass media, application to the Scottish independence referendum

International audienceWe consider a kinetic model describing some mechanisms of opinion formation in the framework of referendums, by allowing that 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. After proving the main properties of the model, such as existence of solutions and conservation properties, 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 orien-tations, is a key ingredient to allow pluralism and prevent consensus. The forecasts of the model are compared to some polls related to the Scottish independence referendum of 2014

THE ROSSELAND LIMIT FOR RADIATIVE TRANSFER IN GRAY MATTER

This paper establishes the Rosseland approximation of the radiative transfer equations in a gray atmosphere, i.e. assuming that the opacity is independent of the radiation frequency

On the exponential decay to equilibrium of the degenerate linear Boltzmann equation

In this paper we study the decay to the equilibrium state for the solution of the linear Boltzmann equation in the torus \T^d=\bR^d/\bZ^{d}, $d \in \N$, by allowing that the non-negative cross section $\sigma$ can vanish in a subregion X:=\{ x \in \T^d\, \vert \, \sigma(x)=0\} of the domain with $\text{meas}(X)\geq 0$ with respect to the Lebesgue measure. We show that the geometrical characterization of $X$ is the key property to produce exponential decay to equilibrium

The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem

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 conditions prescribing the density of particles entering the interval. Under the usual parabolic scaling, a nonlinear diffusion limit is established for this problem. In fact, the techniques presented here allow treating generalizations of the Carleman system where the collision frequency is proportional to some power of the macroscopic density, with exponent in [-1,1]

MATHEMATICAL AND NUMERICAL STUDY OF A DUSTY KNUDSEN GAS MIXTURE

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 existence and 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