Particle approximation of the BGK equation

The BGK equation as the limit of an $N$ particle system

The spatially homogeneous BGK equation is obtained as the limit if a model of a many particle system, similar to Mark Kac's charicature of the spatially homogeneous Boltzmann equation.

Uniqueness of the Non-Equilibrium Steady State for a $1$d BGK model in kinetic theory

We continue our investigation of kinetic models of a one-dimensional gas in contact with homogeneous thermal reservoirs at different temperatures. Nonlinear collisional interactions between particles are modeled by a so-called BGK dynamics which conserves local energy and particle density. Weighting the nonlinear BGK term with a parameter $α\in [0,1]$, and the linearinteraction with the reservoirs by $(1-α)$, we prove that for all $α$ close enough to zero, the explicit spatially uniform non-equilibrium stable state (NESS) is \emph{unique}, and there are no spatially non-uniform NESS with a spa…

A stochastic particle system approximating the BGK equation

We consider a stochastic $N$-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [2], we show that the propagation of chaos does hold and that the one-particle distribution converges to the solution of the BGK equation. The improvement with respect to [2] consists in the fact that here, as suggested by physical considerations, the thermalizing transition is driven only by the restriction of the particle configuration in a small neighborhood of the jumping particle. In other words, the …

从粒子系统到BGK方程

From particle systems to the BGK equation

本文研究DSMC方法对应的非均匀Kac随机粒子系统，通过修改动力学规则推导得出BGK方程，为BGK方程的原始论证提供了数学阐释，补充了相关领域的已有研究结果。

多组分均匀BGK模型的矩方程渐近松弛

Asymptotic Relaxation of Moment Equations for a Multi-Species, Homogeneous BGK Model

本文研究了空间均匀多组分BGK模型的宏观速度、能量和温度矩方程，通过建立组分温度的正下界，证明了解的全局存在唯一性及指数衰减至稳态，并给出数值验证。

具有质量交换的二元粒子碰撞

Binary particle collisions with mass exchange

本文研究了具有质量交换的二元粒子碰撞动力学模型，推导了满足H定理的Boltzmann碰撞算子，并在流体力学极限下计算了粘性修正，证明其符合非平衡态热力学形式体系及Onsager倒易关系。