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TMF, 1988, Volume 77, Number 1, Pages 135–153 (Mi tmf5694)  

This article is cited in 3 scientific papers (total in 3 papers)

Linearization and exact solutions of a class of Boltzmann equations

A. V. Mishchenko, D. Ya. Petrina


Abstract: A Boltzmann equation with scattering cross section that depends on the reciprocal and first power of the modulus of the relative velocity is considered. It is solved by application of a Fourier transformation with respect to the velocity and then separation of the variables. The obtained infinite hierarchy of nonlinear ordinary differential equations is solved by means of the method of Poincaré normal forms, generalized to the infinite-dimensional case. Convergence of the series that represents the solution is proved.

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English version:
Theoretical and Mathematical Physics, 1988, 77:1, 1096–1109

Bibliographic databases:

Received: 11.03.1987

Citation: A. V. Mishchenko, D. Ya. Petrina, “Linearization and exact solutions of a class of Boltzmann equations”, TMF, 77:1 (1988), 135–153; Theoret. and Math. Phys., 77:1 (1988), 1096–1109

Citation in format AMSBIB
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\by A.~V.~Mishchenko, D.~Ya.~Petrina
\paper Linearization and exact solutions of a~class of Boltzmann equations
\jour TMF
\yr 1988
\vol 77
\issue 1
\pages 135--153
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=972487}
\zmath{https://zbmath.org/?q=an:0850.76622|0674.76065}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 77
\issue 1
\pages 1096--1109
\crossref{https://doi.org/10.1007/BF01028686}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1988AD89600013}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. D. Gordevskii, “An approximate two-flow solution to the Boltzmann equation”, Theoret. and Math. Phys., 114:1 (1998), 99–108  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. D. Gordevskii, “Biflow distribution with screw modes”, Theoret. and Math. Phys., 126:2 (2001), 234–249  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. D. Gordevskii, “Vortices in a Gas of Hard Spheres”, Theoret. and Math. Phys., 135:2 (2003), 704–713  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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