标题： 具有碰撞频率、与分子速度模长呈线性关系的一维动力学方程 显示英文标题

标题： The kinetic one-dimensional equation with frequency of collisions, affine depending on the module molecular velocity

摘要： 具有碰撞积分型BGK（Bhatnagar, Gross和Krook）且碰撞频率与分子速度模长成线性关系的一维动力方程被构建。在构建方程时使用了粒子数、动量和能量的守恒定律。变量分离导致特征方程。引入了色散方程组。其行列式称为色散函数。研究了特征方程的连续谱和离散谱。色散方程的零点集构成了特征方程的离散谱。找到了对应于离散谱的动力方程的本征解。在广义函数空间中特征方程的解导致了对应于连续谱的本征函数。以关于所引入动力方程的通解结构定理的形式表述了所进行分析的结果。 显示英文摘要

摘要： The one-dimensional kinetic equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and frequency of collisions affine depending on the module of molecular velocity is constructed. Laws of preservation of number of particles, momentum and energy at construction equation are used. Separation of variables leads to the characteristic equation. The system of the dispersion equations is entered. Its determinant is called as dispersion function. It is investigated continuous and discrete spectra of the characteristic equation. The set of zero of the dispersion equation makes the discrete spectrum of the characteristic equation. The eigen solutions of the kinetic equation corresponding to discrete spectrum are found. The solution of the characteristic equation in space of the generalized functions leads to eigen functions corresponding to the continuous spectrum. Results of the spent analysis in the form of the theorem about structure of the general solution of the entered kinetic equation are formulated.