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

以分子气体动力学为基础，数值研究了气体在微尺度和低压环境中边界任意运动时的行为。特别是对边界运动引起的分子速度分布函数的奇异性进行了澄清，构造了一种能够捕捉奇异性的数值方法。该方法被应用于各种基本问题，如非线性声波的传播和气体中单摆的衰减。

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.