| Инд. авторы: | Suriyawichitseranee A., Grigoriev Y.N., Meleshko S.V. |
| Заглавие: | Group analysis and exact solutions of the spatially homogeneous and isotropic Boltzmann equation with a source term |
| Библ. ссылка: | Suriyawichitseranee A., Grigoriev Y.N., Meleshko S.V. Group analysis and exact solutions of the spatially homogeneous and isotropic Boltzmann equation with a source term // AIP Conference Proceedings. - 2019. - Vol.2153. - Art.020019. - ISSN 0094-243X. |
| Внешние системы: | DOI: 10.1063/1.5125084; РИНЦ: 41692082; SCOPUS: 2-s2.0-85072715115; WoS: 000618061800019; |
| Реферат: | eng: This article is devoted to group analysis of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. Complete group classification with respect to a source function only depending on the independent variables is performed. If a source term includes the dependent variable, then preliminary group classification is given. In the case where the source function also depends on a nonlocal term (number of particles), extension of the equivalence Lie group occurs. Using these equivalence transformations and preliminary group classification, reduced equations are derived, and their generalized BKW-solutions are obtained in an explicit form. © 2019 Author(s). |
| Издано: | 2019 |
| Физ. характеристика: | 020019 |
| Конференция: | Название: International Conference on Modern Treatment of Symmetries, Differential Equations and Applications 2019 Аббревиатура: Symmetry 2019 Город: Nakhon Ratchasima Страна: Thailand Даты проведения: 2019-01-14 - 2019-01-18 |
| Цитирование: | 1. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, Cambridge, 1952). 2. L. V. Ovsiannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978) English translation, W. F. Ames (Academic Press, New York, 1982). 3. T. F. Nonenmacher, J. Appl. Math. Physics (ZAMP) 35, 680-691 (1984). 10.1007/BF00952113 4. M. Krook and T. T. Wu, J. Phys. Fluids 20, 1589-1595 (1977). 10.1063/1.861780 5. Y. N. Grigoriev, S. V. Meleshko, and A. Suriyawichitseranee, Int. J. Nonlin. Mech. 61, 15-18 (2014). 10.1016/j.ijnonlinmec.2014.01.004 6. A. V. Bobylev, Dokl. Akad. Nauk SSSR. 225, 1041-1044 (1975). 7. A. V. Bobylev, Dokl. Akad. Nauk SSSR 231, 571-574 (1976). 8. Y. N. Grigoriev and S. V. Meleshko, Investigation of invariant solutions of the Boltzmann kinetic equation and its models, preprint, Institute of Theoretical and Applied Mechanics (1986). 9. S. V. Meleshko, Methods for Constructing Exact Solutions of Partial Differential Equations, Mathematical and Analytical Techniques with Applications to Engineering (Springer Science+Business Media, New York, 2005). 10. Y. N. Grigoriev, N. H. Ibragimov, V. F. Kovalev, and S. V. Meleshko, Symmetries of Integro-Differential Equations and Their Applications in Mechanics and Plasma Physics, Lecture Notes in Physics, Vol. 806 (Springer, Berlin/Heidelberg, 2010). 11. Y. N. Grigoriev and S. V. Meleshko, Dokl. Akad. Nauk SSSR 297, 323-327 (1987). 12. A. V. Bobylev, Dokl. Akad. Nauk SSSR 225, 1296-1299 (1975). 13. G. Spiga, Phys. Fluids 27, 2599-2600 (1984). 10.1063/1.864558 14. A. Santos and J. J. Brey, Phys. Fluids 29, 1750 (1985). 10.1063/1.865647 |
