Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2018, Volume 195, Number 3, Pages 451–482 (Mi tmf9425)  

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

Group analysis of the one-dimensional Boltzmann equation: III. Condition for the moment quantities to be physically meaningful

K. S. Platonova, A. V. Borovskikh

Lomonosov Moscow State University

Abstract: We present the group classification of the one-dimensional Boltzmann equation with respect to the function $\mathcal F=\mathcal{F}(t,x,c)$ characterizing an external force field under the assumption that the physically meaningful constraints $dx=c dt$, $dc=\mathcal{F} dt$, $dt=0$, and $dx=0$ are imposed on the variables. We show that for all functions $\mathcal{F}$, the algebra is finite-dimensional, and its maximum dimension is eight, which corresponds to the equation with a zero $\mathcal{F}$.

Keywords: Boltzmann equation, symmetry group, gas dynamics equation, equivalence group.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-04066
This research was supported by the Russian Foundation for Basic Research (Grant No. 15-01-04066).


DOI: https://doi.org/10.4213/tmf9425

Full text: PDF file (589 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2018, 195:3, 886–915

Bibliographic databases:

Received: 15.06.2017
Revised: 07.08.2017

Citation: K. S. Platonova, A. V. Borovskikh, “Group analysis of the one-dimensional Boltzmann equation: III. Condition for the moment quantities to be physically meaningful”, TMF, 195:3 (2018), 451–482; Theoret. and Math. Phys., 195:3 (2018), 886–915

Citation in format AMSBIB
\Bibitem{PlaBor18}
\by K.~S.~Platonova, A.~V.~Borovskikh
\paper Group analysis of the~one-dimensional Boltzmann equation: III.~Condition for the~moment quantities to be physically meaningful
\jour TMF
\yr 2018
\vol 195
\issue 3
\pages 451--482
\mathnet{http://mi.mathnet.ru/tmf9425}
\crossref{https://doi.org/10.4213/tmf9425}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3808546}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...195..886P}
\elib{https://elibrary.ru/item.asp?id=34940709}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 195
\issue 3
\pages 886--915
\crossref{https://doi.org/10.1134/S0040577918060077}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000437754600007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049582481}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9425
  • https://doi.org/10.4213/tmf9425
  • http://mi.mathnet.ru/eng/tmf/v195/i3/p451

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. V. Borovskikh, K. S. Platonova, “Group analysis of the one-dimensional Boltzmann equation: IV. Complete group classification in the general case”, Theoret. and Math. Phys., 201:2 (2019), 1614–1643  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. K. S. Platonova, A. V. Borovskikh, “Group analysis of the Boltzmann and Vlasov equations”, Theoret. and Math. Phys., 203:3 (2020), 794–823  mathnet  crossref  crossref  mathscinet  isi  elib
    3. K. S. Platonova, A. V. Borovskikh, “Group analysis of the one-dimensional Boltzmann equation. Invariants and the problem of moment system closure”, Theoret. and Math. Phys., 208:3 (2021), 1165–1181  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:188
    Full text:15
    References:17
    First page:9

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021