The aim of this paper is to study a one-dimensional model system of equations for ionized gas dynamics at high temperature where the gas is a mixture of two kinds of monatomic gas. In addition to the mass density, pressure, temperature and particle velocity, degrees of ionization of both gases are also involved. The equations of motion are derived from conservation of mass, momentum and energy, which are supplemented by the first and second law of thermodynamics, thermodynamic equations and Saha’s ionization equations by assuming that the local thermal equilibrium is attained. The equations constitute a strictly hyperbolic system, which guarantees that the initial value problem is well-posed locally in time for sufficiently smooth initial data. However the geometric properties of the system are rather complicated: In particular, we prove the existence of a region where convexity (genuine nonlinearity) fails for forward and backward characteristic fields. Also we study thermodynamic properties of shock waves by detailed analyses of the Hugoniot locus, which are used in a mathematical study of existence and uniqueness of solutions to the shock tube problem.

本文的目的是研究高温下的电离气体动力学方程的一维模型系统，其中气体是两种单原子气体的混合物。除了质量密度，压力，温度和粒子速度外，还涉及两种气体的电离度。运动方程式是从质量守恒，动量守恒和能量守恒中得出的，并假设达到局部热平衡，并由热力学第一定律和第二定律，热力学方程式和萨哈电离方程式补充。这些方程式构成了严格的双曲系统，它保证了初始值问题可以在时间上局部地适当定位，以使初始数据足够平滑。但是，系统的几何属性相当复杂：特别是，我们证明了存在一个区域，其中正向和反向特征场的凸性（真正的非线性）失效。另外，我们通过对Hugoniot轨迹的详细分析来研究冲击波的热力学性质，这些数学分析用于对冲击管问题的解的存在和唯一性进行数学研究。