二元Maxwell混合气体Boltzmann H定理的一般化(英文)

Generalization of the Boltzmann H-theorem for Binary Mixtures of Maxwell Gases

本文给出了二元Maxwell混合气体Boltzmann方程组并讨论了Boltzmann H定理的一般化,得出建立在空间各向同性Boltzmann方程组解空间上且随时间单调递减的一组凸函数的充分条件.为此,我们先对二元Maxwell混合气体Boltzmann方程组和分布函数进行了Fourier变换,然后分析了Boltzmann方程组解空间上随时间单调递减的函数的特征.通过一条定理论证了一般化的Boltzmann H函数的充分条件对任意维轴对称的解都成立.

Boltzmann equations and generalization of the Boltzmann H -theorem for binary mixtures of Maxwell gases are discussed. Sufficient conditions for convex and isotropic functions, which are defined on the solution space of the spatially homogeneous Boltzmann equations, are given in the present paper. These functions are monotonically decreasing with time. The distribution functions and the Boltzmann equations for binary mixtures of Maxwell gases are processed by Fourier transform at first. Then, the functions with the monotonic behavior along time for the Boltzmann equations are characterized. In addition, a theorem shows that the sufficient conditions valid for axially symmetric solutions in any dimension.