波茲曼方程及其邊界奇點綜述

Abstract

波茲曼方程是描述熱力學系統演化的重要數學模型。數學家已將其廣泛應用在各個科學領域，並對其進行了許多的研究。在本文中，我們回顧了波茲曼方程碰撞算子的性質。我們主要關注於 Milne 和 Kramers 問題的解的存在性，唯一性和漸近行為。我們也介紹近期線性波茲曼方程的宏觀變量的邊界奇點方面的工作。

The Boltzmann Equation is an important mathematical model that describes the evolution of a thermodynamic system. It has been studied and applied in various scientific areas. In this article, we review the properties of collision operator of Boltzmann equation. We will focus mainly on the well-posedness and the asymptotic behaviour of the Milne and Kramers problem as well as the recent work in the boundary singularity of macroscopic variables for linearized Boltzmann equation.