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TMF, 1984, Volume 60, Number 2, Pages 280–310 (Mi tmf5284)  

This article is cited in 7 scientific papers (total in 7 papers)

Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas

A. V. Bobylev


Abstract: Results obtained in recent years in the theory of the nonlinear Boltzmann equation for Maxwellian molecules are reviewed. The general theory of spatially homogeneous relaxation based on Fourier transformation with respect to the velocity is presented. The behavior of the distribution function $f({\mathbf v},t)$ is studied in the limit $|{\mathbf v}|\rightarrow\infty$ (the formation of the MaxwelIian tails) and $t\rightarrow\infty$ (relaxation rate). An analytic transformation relating the nonlinear and linearized equations is constructed. It is shown that the nonlinear equation has a countable set of invariants, families of particular solutions of special form are constructed, and an analogy with equations of Korteweg–de Vries type is noted.

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English version:
Theoretical and Mathematical Physics, 1984, 60:2, 820–841

Bibliographic databases:

Received: 03.05.1984

Citation: A. V. Bobylev, “Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas”, TMF, 60:2 (1984), 280–310; Theoret. and Math. Phys., 60:2 (1984), 820–841

Citation in format AMSBIB
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\by A.~V.~Bobylev
\paper Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas
\jour TMF
\yr 1984
\vol 60
\issue 2
\pages 280--310
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=762269}
\zmath{https://zbmath.org/?q=an:0565.76074}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 60
\issue 2
\pages 820--841
\crossref{https://doi.org/10.1007/BF01018983}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984ACL9200011}


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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. V. Vedenyapin, “Differential forms in spaces without a norm. A theorem on the uniqueness of Boltzmann's $H$-function”, Russian Math. Surveys, 43:1 (1988), 193–219  mathnet  crossref  mathscinet  zmath  adsnasa
    2. A. V. Mishchenko, D. Ya. Petrina, “Linearization and exact solutions of a class of Boltzmann equations”, Theoret. and Math. Phys., 77:1 (1988), 1096–1109  mathnet  crossref  mathscinet  zmath  isi
    3. A. A. Raines, “Numerical testing of Bird's VHS model”, Comput. Math. Math. Phys., 35:8 (1995), 1025–1031  mathnet  mathscinet  zmath  isi
    4. M. S. Ivanov, M. A. Korotchenko, G. A. Mikhailov, S. V. Rogazinskii, “Global weighted Monte Carlo method for the nonlinear Boltzmann equation”, Comput. Math. Math. Phys., 45:10 (2005), 1792–1801  mathnet  mathscinet
    5. M. A. Korotchenko, G. A. Mikhailov, S. V. Rogazinskii, “Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations”, Comput. Math. Math. Phys., 47:12 (2007), 2023–2033  mathnet  crossref  mathscinet
    6. Malkov E.A., Ivanov M.S., “Determinirovannyi metod chastits-v-yacheikakh dlya resheniya zadach dinamiki razrezhennogo gaza. chast i”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 12:1 (2011), 368–374  mathnet  mathnet  elib
    7. Evsevleeva L.G., Sverdlova O.L., Kirik M.S., Gozbenko V.E., “Analiticheskaya model vzaimodeistviya atomov kisloroda s poverkhnostyu adsorbenta”, Sovremennye tekhnologii. sistemnyi analiz. modelirovanie, 2012, no. 3, 137–140  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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