We introduce and discuss a kinetic model for wealth distribution in a simple market economy which is built of a number of countries or social groups. Our approach is based on the model with risky investments introduced by Cordier, Pareschi and one of the authors in [13] and borrows ideas from...

In this paper, we introduce and discuss the passage to hydrodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the knowledge...

Kinetic market models have been proposed recently to account for the redistribution of wealth in simple market economies. These models allow to develop a qualitative theory, which is based on methods borrowed from the kinetic theory of rarefied gases. The aim of these notes is to present a...

The development of Langevin models for molecular dynamics represents a promising approach to deal with the cost issue of Boltzmann equation solutions. A recent paper of Zhang et al. suggested to study the Prandtl number variability of such molecular Langevin models under equilibrium conditions....

In this article we present a fluid dynamical model for the charge transport in semiconductors based on a recently found asymptotic solution of the semiconductor Boltzmann transport equation (BTE) for strong fields.

The controversial problem of the evolution of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated by a piston whose mass is equal to the...

This paper is concerned with generalizations of the known local Lagrange formalism of first order. It will be applied to kinetic equations like the Fokker-Planck equation and the Boltzmann equation. In the latter case nonlocal methods are necessary from the very beginning. Nevertheless, in the...

The present paper considers a detailed analysis of the nonequilibrium effects for a model reactive system with the Chapman–Eskog (CE) solution of the Boltzmann equation as well as an explicit time dependent solution. The elastic cross sections employed are a hard sphere cross section and the...

A kinetic approach to a mixture of gases whose particles interact by elastic scattering and by a bimolecular chemical reaction is analyzed by means of the relevant Boltzmann-like equation. Conservation laws and moment equations are considered, and, improving previous results in the literature,...

A mixture of relativistic gases of non-disparate rest masses in a Schwarzschild metric is studied on the basis of a relativistic Boltzmann equation in the presence of gravitational fields. A BGK-type model equation of the collision operator of the Boltzmann equation is used in order to compute...