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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 170, Number 3, Pages 481–488
DOI: https://doi.org/10.4213/tmf6780 (Mi tmf6780) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Stationary solutions of the kinetic Broadwell model

O. V. Ilyin

Dorodnitsyn Computation Center, RAS, Moscow, Russia
Full-text PDF (339 kB) Citations (10)
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DOI: https://doi.org/10.4213/tmf6780
Abstract: We consider a stationary discrete model of the Boltzmann equation for four velocities (the Broadwell model). We obtain new exact automodel solutions of the model corresponding to an incompressible and a compressible gas. We show that one class of solutions satisfies the problem of gas evaporation and condensation on the boundary of a disk and external space. The system turns out to be strongly nonequilibrium, and continuous medium equations are not applicable to it.
Keywords: kinetic Broadwell model, automodel solution.
Received: 10.04.2011
English version:
Theoretical and Mathematical Physics, 2012, Volume 170, Issue 3, Pages 406–412
DOI: https://doi.org/10.1007/s11232-012-0039-0
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: O. V. Ilyin, “Stationary solutions of the kinetic Broadwell model”, TMF, 170:3 (2012), 481–488; Theoret. and Math. Phys., 170:3 (2012), 406–412
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6780
  • https://www.mathnet.ru/eng/tmf/v170/i3/p481
    • This publication is cited in the following 10 articles:
    1. S. A. Dukhnovskii, “Uslovie sekulyarnosti kineticheskoi sistemy Broduella”, Materialy 6 Mezhdunarodnoi konferentsii «Dinamicheskie sistemy i kompyuternye nauki: teoriya i prilozheniya» (DYSC 2024). Irkutsk, 16–20 sentyabrya 2024 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 238, VINITI, M., 2025, 49–58  mathnet  crossref
    2. S. A. Dukhnovskii, “Gruppovoi analiz sistemy McKean”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 232, VINITI RAN, M., 2024, 153–157  mathnet  crossref
    3. S. A. Dukhnovskii, “Uslovie sekulyarnosti dlya sistemy McKean”, Materialy Mezhdunarodnoi konferentsii  «Klassicheskaya i sovremennaya geometriya»,  posvyaschennoi 100-letiyu so dnya rozhdeniya  professora Levona Sergeevicha Atanasyana  (15 iyulya 1921 g.—5 iyulya 1998 g.). Moskva, 1–4 noyabrya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 220, VINITI RAN, M., 2023, 44–48  mathnet  crossref
    4. S. A. Dukhnovskii, “Painlevé Test and a Self-Similar Solution of the Kinetic Model”, J Math Sci, 275:5 (2023), 613  crossref
    5. Sergey Dukhnovsky, “A self-similar solution for the two-dimensional Broadwell system via the Bateman equation”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, no. 3, 30–40  mathnet  crossref  mathscinet
    6. S. A. Dukhnovskii, “Approksimatsionnoe reshenie sistemy McKean”, Materialy Voronezhskoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 191, VINITI RAN, M., 2021, 157–161  mathnet  crossref  elib
    7. S. A. Dukhnovskii, “Test Penleve i avtomodelnoe reshenie kineticheskoi modeli”, Materialy XVII Vserossiiskoi molodezhnoi shkoly-konferentsii «Lobachevskie chteniya-2018»,  23-28 noyabrya 2018 g., Kazan.  Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 176, VINITI RAN, M., 2020, 91–94  mathnet  crossref  elib
    8. S. A. Dukhnovskii, “Resheniya sistemy Karlemana cherez razlozhenie Penleve”, Vladikavk. matem. zhurn., 22:4 (2020), 58–67  mathnet  crossref  elib
    9. Sergey Dukhnovsky, “On solutions of the kinetic McKean system”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 3, 3–11  mathnet
    10. O. V. Ilyin, “Symmetries, the current function, and exact solutions for Broadwell's two-dimensional stationary kinetic model”, Theoret. and Math. Phys., 179:3 (2014), 679–688  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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