Abstract:
The use of Case's method and singular integral equations in the solution of model Boltzmann equations for rarefied-gas dynamics is demonstrated. Exact solutions of the Boltzmann equation with BGK (Bhatnagar–Gross–Krook) collision operator are obtained for the first time in the problem of weak evaporation and in the problem of temperature and density discontinuities; an exact solution of the Boltzmann equation with collision operator of mixed type in the Kramers problem is also obtained. For the scalar BGK Boltzmann equation, the simplest known exact solution of the Kramers problem is obtained. For this, an expansion of a polynomial of arbitrary degree in the eigenfunctions of the corresponding characteristic equation is demonstrated.
Citation:
A. V. Latyshev, “Analytic aspects of solution of model kinetic equations”, TMF, 85:3 (1990), 428–442; Theoret. and Math. Phys., 85:3 (1990), 1311–1321
This publication is cited in the following 10 articles:
A. V. Latyshev, A. A. Yushkanov, “Thirteen-moments model kinetic equation and its parameters”, Math. Models Comput. Simul., 9:2 (2017), 169–175
A. V. Latyshev, V. N. Popov, A. A. Yushkanov, “Primenenie metoda Keiza v zadache o teplovom skolzhenii razrezhennogo gaza
vdol tverdoi sfericheskoi poverkhnosti”, Sib. zhurn. industr. matem., 5:3 (2002), 103–114
A. V. Latyshev, A. A. Yushkanov, “Weak evaporation (condensation) with an arbitrary evaporation coefficient in gases with a constant frequency of molecular collisions”, J Eng Phys Thermophys, 73:3 (2000), 528
A. V. Latyshev, O. V. Timchenko, “Theory and accurate solutions of the problem of the isothermal slip of a medium-density binary gas”, Comput. Math. Math. Phys., 35:4 (1995), 459–469
A. V. Latyshev, A. A. Yushkanov, “Analytic solution to the problem of the temperature jump in a gas with rotational degrees of freedom”, Theoret. and Math. Phys., 95:3 (1993), 758–765
A. V. Latyshev, A. A. Yushkanov, “Analytic solution of a problem on the resistance of the interface between crystallites”, Comput. Math. Math. Phys., 33:4 (1993), 543–551
A. V. Latyshev, A. G. Lesskis, A. A. Yushkanov, “Exact solution to the behavior of the electron plasma in a metal layer in an alternating electric field”, Theoret. and Math. Phys., 90:2 (1992), 119–126
A. V. Latyshev, A. A. Yushkanov, “Analytic solution of boundary-value problems for nonstationary model kinetic equations”, Theoret. and Math. Phys., 92:1 (1992), 782–790
A. V. Latyshev, “Analytic solution of the ellipsoidal-statistical model Boltzmann equation”, Fluid Dyn, 27:2 (1992), 267
A. V. Latyshev, “Analytic solution of slip problems for a binary gas”, Theoret. and Math. Phys., 86:3 (1991), 276–289
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