Theoretical and Mathematical Physics

, Volume 97, Issue 2, pp 1299–1311 | Cite as

Analytic solution of vector model kinetic equations with constant kernel and their applications

  • A. V. Latyshev


Exact solutions are obtained for the first time for the half-space boundary-value problem for the vector model kinetic equations
$$\begin{gathered} \mu \frac{\partial }{{\partial x}}\Psi (x,\mu ) + \sum \Psi (x,\mu ) = C\int_{ - \infty }^\infty {\exp ( - } \mu '^2 )\Psi (x,\mu ')d\mu ', \hfill \\ \mathop {\lim }\limits_{x \to 0 + } \Psi (x,\mu ) = \Psi _0 (\mu ), \mu > 0, \mathop {\lim }\limits_{x \to + 0} \Psi (x,\mu ) = {\rm A}, \mu< 0, \hfill \\ \end{gathered}$$
$$x > 0, \mu \in ( - \infty , 0) \cup (0, + \infty ), \sum = diag\{ \sigma _1 ,\sigma _2 \} ,$$
C=[cij] is a square second-order matrix, and ψ(x, μ) is a vector column with the elements ψ1(x,μ) and ψ2(x,μ). As an application, an exact solution is obtained for the first time to the problem of the diffusion slip of a binary gas for a model Boltzmann equation with collision operator in the form proposed by MacCormack.


Exact Solution Kinetic Equation Boltzmann Equation Vector Column Vector Model 
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© Plenum Publishing Corporation 1994

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  • A. V. Latyshev

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