Mathematical and physical study of moving boundary problems for the Boltzmann equation

基于分子气体动力学，对微尺度下低压气体在边界任意运动时的行为进行了数值研究。特别是，在分子速度分布函数的奇异性所造成的边界的运动进行了澄清，并能够捕获的奇异性的数值方法被构造。该方法被应用到各种基本问题，如非线性声波的传播和气体中的钟摆的衰减。

The behavior of a gas in microscales and in low-pressure circumstances when the boundary is moving arbitrarily was investigated numerically on the basis of molecular gas dynamics. In particular, the singularities in the molecular velocity distribution function caused by the motion of the boundary were clarified, and a numerical method that is able to capture the singularities was constructed. The method was applied to various fundamental problems, such as the propagation of nonlinear acoustic waves and the decay of a pendulum in the gas.