振荡面上气体行为的第二类斯托克斯问题的解析解。第一部分：特征值和特征解
Analytical solution of the second Stokes problem on behavior of gas over a oscillation surface. Part I: eigenvalues and eigensolutions
摘要：
建立了充入半空间的稀薄气体的第二Stokes问题。一个限制半空间的平面在平面内作和谐的振荡。采用τ模型形式的碰撞积分动力学方程。考虑了气体分子从壁面漫反射的情况。初始动力学方程存在本征解（连续模），对应于连续谱.研究了色散函数的性质。研究了复平面上色散函数零点构成的该问题的离散谱。证明了色散函数零点的个数与问题系数的指数相等。问题系数被理解为实轴上从上到下的色散函数的边界值之间的关系。此外，初始动力学方程存在本征解（离散模式），对应于离散谱。求出了动力学方程的本征解展开形式的通解，其未知系数分别对应于离散谱和连续谱。
英文摘要：
The second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with modelling integral of collisions in the form tau-model is used. The case of diffusive reflection of molecules of gas from a wall is considered. There are eigen solutions (continuous modes) the initial kinetic equation, corresponding to the continuous spectrum. Properties of dispersion function are studied. The discrete spectrum of this problem consisting of zeroes of dispersion function in complex plane is investigated. It is shown, that number of zero of dispersion function to equally doubled index of coefficient of the problem. The problem coefficient is understood as the relation of boundary values of dispersion function from above and from below on the real axis. Further there are eigen solutions (discrete modes) the initial kinetic equation, corresponding to the discrete spectrum. The common solution of the kinetic equation in the form of expansion by eigensolutions with the unknown coefficients corresponding to discrete and continuous spectra is worked out.
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