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 TMF, 1991, Volume 86, Number 3, Pages 402–419 (Mi tmf5457)

Analytic solution of slip problems for a binary gas

A. V. Latyshev

Abstract: Exact solutions are obtained for the first time for the system of $\tau$-model Boltzmann equations for a binary gas in problems of slip, namely, the isothermal, thermal, diffusion, Burnett thermal, and Burnett diffusion solutions. Cases of complete and partial accommodation of the tangential momentum of the molecules are considered. The model Boltzmann equations are reduced to a Wiener–Hopf equation of the first kind with two kernels (one kernel has a direct shift, the other an inverse shift). This equation is reduced by an inverse Laplace transformation to a Carleman boundary-value problem with inverse shift, the solution of which is given by Neumann series. In the case of complete accommodation, the solution can be given in closed form.

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English version:
Theoretical and Mathematical Physics, 1991, 86:3, 276–289

Bibliographic databases:

Citation: A. V. Latyshev, “Analytic solution of slip problems for a binary gas”, TMF, 86:3 (1991), 402–419; Theoret. and Math. Phys., 86:3 (1991), 276–289

Citation in format AMSBIB
\Bibitem{Lat91} \by A.~V.~Latyshev \paper Analytic solution of slip problems for a~binary gas \jour TMF \yr 1991 \vol 86 \issue 3 \pages 402--419 \mathnet{http://mi.mathnet.ru/tmf5457} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1107940} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 86 \issue 3 \pages 276--289 \crossref{https://doi.org/10.1007/BF01028426} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GJ55400010} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. 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
2. A. V. Latyshev, “The solution of boundary-value problems for the equations of radiation transfer”, Comput. Math. Math. Phys., 34:2 (1994), 193–203
3. 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
4. A. V. Latyshev, A. A. Yushkanov, “The Kramers problem for the ellipsoidal-statistical Boltzmann equation with frequency proportional to the velocity of molecules”, Comput. Math. Math. Phys., 37:4 (1997), 471–481
5. N. B. Engibaryan, A. Kh. Khachatryan, “Some convolution-type integral equations in kinetic theory”, Comput. Math. Math. Phys., 38:3 (1998), 452–467
6. N. B. Engibaryan, A. Kh. Khachatryan, “Voprosy nelineinoi teorii dinamiki razrezhennogo gaza”, Matem. modelirovanie, 16:1 (2004), 67–74
7. A. V. Latyshev, A. A. Yushkanov, “Novyi metod resheniya granichnykh zadach kineticheskoi teorii”, Zh. vychisl. matem. i matem. fiz., 52:3 (2012), 539–552
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