Stationary solutions of the kinetic Broadwell model
Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 481-488 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
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O. V. Ilyin. Stationary solutions of the kinetic Broadwell model. Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 481-488. http://geodesic.mathdoc.fr/item/TMF_2012_170_3_a11/

[1] J. Broadwell, J. Fluid Mech., 19 (1964), 401–414 | DOI | MR | Zbl

[2] H. Cornille, J. Phys. A, 20:16 (1987), L1063–L1067 | DOI | MR

[3] H. Cornille, J. Statist. Phys., 52:3–4 (1988), 897–949 | DOI | MR | Zbl

[4] A. V. Bobylev, G. Spiga, J. Phys. A, 27:22 (1994), 7451–7459 | DOI | MR | Zbl

[5] A. V. Bobylev, G. Caraffini, G. Spiga, Eur. J. Mech. B/Fluids, 19:2 (2000), 303–315 | DOI | MR | Zbl

[6] A. V. Bobylev, Math. Meth. Appl. Sci., 19 (1996), 825–845 | 3.0.CO;2-1 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[7] H. Cabannes, Eur. J. Mech. B/Fluids, 16:1 (1997), 1–15 | MR | Zbl

[8] O. Lindblom, N. Eiler, TMF, 131:2 (2002), 179–193 | DOI | MR | Zbl

[9] A. Bobylev, G. Toscani, Contin. Mech. Thermodyn., 8:5 (1996), 257–274 | DOI | MR | Zbl

[10] V. Aristov, O. Ilyin, Phys. Lett. A, 374:43 (2010), 4381–4384 | DOI | Zbl

[11] V. Aristov, Zh. vychisl. matem. i matem. fiz., 44:6 (2004), 1127–1140 | MR | Zbl

[12] F. Golse, Commun. Partial Differ. Equations, 12:3 (1987), 315–326 | DOI | MR | Zbl

[13] C. Cercignani, R. Illner, M. Shinbrot, Commun. Math. Phys., 114:4 (1988), 687–698 | DOI | MR | Zbl

[14] M. Kogan, Dinamika razrezhennogo gaza, Nauka, M., 1967 | Zbl

[15] V. Aristov, Phys. Lett. A, 250:4–6 (1998), 354–359 | DOI