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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2018, Volume 59, Issue 2, Pages 3–11
DOI: https://doi.org/10.15372/PMTF20180101 (Mi pmtf590) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Exact solutions of the Boltzmann equations with a source

Yu. N. Grigor'evab, S. V. Meleshkoc, A. Suriyawichitseraneec

a Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia
c School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand
Full-text PDF (234 kB) Citations (7)
DOI: https://doi.org/10.15372/PMTF20180101
Abstract: Exact solutions of a nonlinear Boltzmann kinetic equation with a source are constructed in the case of an isotropic distribution function and Maxwell model of isotropic scattering. These solutions are constructed with the use of an equivalence group such that one of its transformations uniquely identifies the class of the source functions that are linear in terms of the distribution function; moreover, the transformed equation has a zero right side. As a result, one can explicitly find invariant solutions of the type of the Bobylev–Krook–Wu solutions, in particular, those that admit physical interpretation.
Keywords: Boltzmann equation, isotropic distribution function, source function, invariant solutions.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00209а
Received: 17.04.2017
English version:
Journal of Applied Mechanics and Technical Physics, 2018, Volume 59, Issue 2, Pages 189–196
DOI: https://doi.org/10.1134/S0021894418020013
Bibliographic databases:
Document Type: Article
UDC: 532.5:532.517.4
Language: Russian
Citation: Yu. N. Grigor'ev, S. V. Meleshko, A. Suriyawichitseranee, “Exact solutions of the Boltzmann equations with a source”, Prikl. Mekh. Tekh. Fiz., 59:2 (2018), 3–11; J. Appl. Mech. Tech. Phys., 59:2 (2018), 189–196
Citation in format AMSBIB
\Bibitem{GriMelSur18}
\by Yu.~N.~Grigor'ev, S.~V.~Meleshko, A.~Suriyawichitseranee
\paper Exact solutions of the Boltzmann equations with a source
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2018
\vol 59
\issue 2
\pages 3--11
\mathnet{http://mi.mathnet.ru/pmtf590}
\crossref{https://doi.org/10.15372/PMTF20180101}
\elib{https://elibrary.ru/item.asp?id=32773488}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2018
\vol 59
\issue 2
\pages 189--196
\crossref{https://doi.org/10.1134/S0021894418020013}
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  • https://www.mathnet.ru/eng/pmtf/v59/i2/p3
    • This publication is cited in the following 7 articles:
    1. Fubiao Lin, Yang Yang, Xinxia Yang, “Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis”, Symmetry, 16:1 (2024), 65  crossref
    2. Yurii N. Grigoryev, Sergey V. Meleshko, “Equivalence group and exact solutions of the system of nonhomogeneous Boltzmann equations”, Continuum Mech. Thermodyn., 35:5 (2023), 2117  crossref
    3. Patrick O'Rourke, Scott Ramsey, Brian Temple, “Lie Group Analysis of the Integral Equations Related to Neutron Slowing-Down Theory”, Nuclear Science and Engineering, 196:7 (2022), 792  crossref
    4. M.R. Davletshina, A.S. Chiglintseva, “NUMERICAL STUDY OF THE FAILURE OF A SPHERICAL HYDRATE MONOLITH”, ntj-oil, 2021, no. 6, 42  crossref
    5. Fubiao Lin, Qianhong Zhang, “Symmetries and exact solutions of the population balance equation with growth and breakage processes, using group analysis”, Math Methods in App Sciences, 44:5 (2021), 3913  crossref
    6. Fubiao Lin, Qianhong Zhang, “Exact solutions of population balance equations for breakage and growth processes, using group analysis”, Applied Mathematics and Computation, 368 (2020), 124790  crossref
    7. Nail G. Musakaev, Stanislav L. Borodin, Denis S. Belskikh, “Calculation of the Parameters for the Process of Gas Injection into a Reservoir Saturated with Methane and Its Hydrate”, TSU Herald. Phys Math Model. Oil, Gas, Energy, 4:3 (2018), 165  crossref
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