Analytic Solutions of Boundary Value Problems for Model Kinetic Equations

Anatolii V. Latyshev and Alexander A. Yushkanov
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Anatolii V. Latyshev: Moscow Pedagogical University
Alexander A. Yushkanov: Moscow Pedagogical University

A chapter in Mathematical Modeling, 2001, pp 17-24 from Springer

Abstract: Abstract Our review will be dedicated to the analysis of the analytic solutions of model kinetic equations for one-component gas. Such solutions may be obtained only for linearized problems. So we will consider linearized form of kinetic equations. All equations will be represented in dimensionless form for simplicity. The most known model kinetic equations are: BKW-equation (Boltzmann, Krook, Welander)1,2, ES-equation3, and Shakhov equation4. These equations may be combined in the general equation $$\frac{{\partial h}}{{\partial t}} + \vec v\frac{{\partial h}}{{\partial \vec r}} + h(\vec r,\vec v,t) = N(\vec r,t) + 2\vec v\vec G(\vec r,t) + ({v^2} - \frac{3}{2})T(\vec r,t) + \omega \sum\limits_{i,j = 1}^3 {{v_i}} {v_j}{P_{i,j}}(\vec r,t) + (1 - \frac{{\Pr }}{\beta })\sum {v_i}({v^2} - \frac{5}{2}){Q_i}(\vec r,t).$$

Date: 2001
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DOI: 10.1007/978-1-4757-3397-6_2

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