特征方程本征函数正交理论作为模型动力学方程边值问题的一种解法
Theory of orthogonality of eigenfunctions of the characteristic equations as a method of solution boundary problems for model kinetic equations
摘要：
本文考虑两类线性动力学方程：碰撞频率为常数，气体分子平均自由程为常数（即，分子碰撞的频率，与模量分子速度成比例）。基于系数等于边值色散函数之比的齐次Riemann边值问题，建立了相应特征方程的广义奇异本征函数的半空间正交性理论，从而导出了分离变量法。并在这两个边值问题的动力学理论（扩散轻组分的二元气体和Kramers问题的等温滑移）显示的应用理论正交特征函数的解析解这些任务。
英文摘要：
We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous Riemann boundary value problem with a coefficient equal to the ratio of the boundary values dispersion function, develops the theory of the half-space orthogonality of generalized singular eigenfunctions corresponding characteristic equations, which leads separation of variables. And in this two boundary value problems of the kinetic theory (diffusion light component of a binary gas and Kramers problem about isothermal slip) shows the application of the theory orthogonality eigenfunctions for analytical solutions these tasks.
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