Brey, J. J.; Santos, A. Solution of the BGK model kinetic equation for very hard particle interaction. (English) Zbl 0589.76099 J. Stat. Phys. 37, 123-150 (1984). Summary: We study the Bhatnagar-Gross-Krook model kinetic equation with a velocity-dependent collision frequency. We derive the conditions that must be verified in order to keep the main physical properties of the Boltzmann equation, i.e., H-theorem and conservation laws. The particular case of the so-called VHP interaction is considered, and the resulting kinetic equation is solved for a homogeneous and isotropic gas. Overpopulation phenomena are observed and analyzed for some kinds of initial conditions. The results are compared, where possible, with the exact solution of the Boltzmann equation. Cited in 2 Documents MSC: 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 82B05 Classical equilibrium statistical mechanics (general) 82B40 Kinetic theory of gases in equilibrium statistical mechanics Keywords:BGK model kinetic equation; Tjon effect; velocity-dependent collision frequency; Boltzmann equation; H-theorem; conservation laws; VHP interaction; homogeneous and isotropic gas; Overpopulation phenomena; initial conditions; exact solution PDF BibTeX XML Cite \textit{J. J. Brey} and \textit{A. Santos}, J. Stat. Phys. 37, 123--150 (1984; Zbl 0589.76099) Full Text: DOI OpenURL References: [1] For a review, see M. H. Ernst, inFundamental Problems in Statistical Mechanics V, E.G. D. Cohen, ed. (North-Holland, Amsterdam, 1980);Phys. Rep. 78:1 (1981); inNonequilibrium Phenomena I. The Boltzmann Equation, J. L. Lebowitz and E. W. Montroll, eds. (North-Holland, Amsterdam, 1983). [2] J. A. Tjon,Phys. Lett. 70A:369 (1979). [3] M. H. Ernst and E. M. Hendriks,Phys. Lett. 81A:315, 371 (1981); E. Futcher, M. R. Hoare, E. M. Hendriks, and M. H. Ernst,Physica 101A:185 (1980); E. M. Hendriks and T. M. Nieuwenhuizen,J. Stat. Phys. 29:591 (1982); Th. W. Ruijgrok and T. T. Wu,Physica 113A:401 (1982). [4] C. Cercignani,Theory and Applications of the Boltzmann Equation (Scottish Academic Press, Edinburgh, 1975). · Zbl 0403.76065 [5] M. H. Ernst and E. M. Hendriks,Phys. Lett. 70A:183 (1979); E. M. Hendriks and M. H. Ernst,Physica 102A:101, 119 (1982). [6] E. H. Hauge,Phys. Lett. 74A:183 (1979); E. H. Hauge and E. Praestgaard,J. Stat. Phys. 24:21 (1981). [7] G. E. Uhlenbeck and G. W. Ford,Lectures in Statistical Mechanics (American Mathematical Society, Providence, Rhode Island, 1963). · Zbl 0111.43802 [8] A. V. Bobylev,Dokl. Akad. Nauk SSSR 225:1041, 1296 (1975);231:571 (1976) [Sov. Phys.-Dokl. 20:820, 822 (1976);21:632 (1976)]. [9] M. Krook and T. T. Wu,Phys. Rev. Lett. 36:1107 (1976);38:991 (1977);Phys. Fluids 20:1589 (1977). [10] M. H. Ernst,Phys. Lett. 69A:390 (1979); M. Barnsley and H. Cornille,J. Math. Phys. 21:176 (1980). [11] H. Cornille and A. Gervois,J. Stat. Phys. 23:167 (1980). [12] J. J. Brey, J. Gómez Ordoñez, and A. Santos,Phys. Rev. A 26:2817 (1982);Mol. Phys. 50:1163 (1983);J. Chem. Phys. 80: 5155 (1984). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.