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Boundary value problems for the ellipsoidal statistical equation. (Russian) Zbl 1071.76048
The article is devoted to studying the so-called half-space boundary value problems for the ellipsoidal statistical equation with the collision frequency \(\nu = \nu_0V\), where \(V\) is the molecular velocity modulus which arises in the context of the kinetic theory of rarefied gas flows. The main aim of the article is to present a method for analytical solution of the above-mentioned boundary value problems. As a result, the authors obtain a solution to the classical Smoluchowski problem on the temperature jump and weak evaporation in a rarefied gas. Moreover, formulas for calculating the temperature jump and the concentration are presented. Numerical representations of the formulas obtained make it possible to determine the coefficient \(C_t\) of the temperature jump and to perform a comparison with previous results.
MSC:
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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