Related papers: Kinetic models with randomly perturbed binary coll…
Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas…
We propose and investigate general kinetic models %of Boltzmann type with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. These models can be applied to many…
Boltzmann equation requires some alternative simpler kinetic model like BGK to replace the collision term. Such a kinetic model which replaces the Boltzmann collision integral should preserve the basic properties and characteristics of the…
We introduce a system of kinetic equations describing an exchange market consisting of two populations of agents (dealers and speculators) expressing the same preferences for two goods, but applying different strategies in their exchanges.…
Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability…
We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown…
We study the boundary value problem of two stationary BGK-type models - the BGK model for fast chemical reaction and the BGK model for slow chemical reaction - and provide a unified argument to establish the existence and uniqueness of…
This paper deals with a one--dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter $p>0$. In particular, the paper provides bounds for certain distances…
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the…
Many features of granular media can be modelled as a fluid of hard spheres with {\em inelastic} collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations. At low-density, a…
We consider a kinetic equation describing evolution of a particle distribution function in a system with nonlinear wave-particle interactions (trappings into a resonance and nonlinear scatterings). We study properties of its solutions and…
In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…
We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time…
We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of…
We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…
We discuss a family of models expressed by nonlinear differential equation systems describing closed market societies in the presence of taxation and redistribution. We focus in particular on three example models obtained in correspondence…
We analyse the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the non-equilibrium steady state reached by the system. Here, we…
The aim of this paper is to study large deviations for the self-similar solution of a Kac-type kinetic equation. Under the assumption that the initial condition belongs to the domain of normal attraction of a stable law of index $\alpha <2$…
This paper deals with a class of Boltzmann equations on the real line, extensions of the well-known Kac caricature. A distinguishing feature of the corresponding equations is that therein, the collision gain operators are defined by…
This paper considers the ideal gas-like model of trading markets, where each individual is identified as a gas molecule that interacts with others trading in elastic or money-conservative collisions. Traditionally this model introduces…