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Stationary solutions of the kinetic Broadwell model

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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.

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References

  1. J. Broadwell, J. Fluid Mech., 19, 401–414 (1964).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. H. Cornille, J. Phys. A, 20, L1063–L1067 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  3. H. Cornille, J. Statist. Phys., 52, 897–949 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. A. V. Bobylev and G. Spiga, J. Phys. A, 27, 7451–7459 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. A. V. Bobylev, G. Caraffini, and G. Spiga, Eur. J. Mech. B/Fluids, 19, 303–315 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. V. Bobylev, Math. Meth. Appl. Sci., 19, 825–845 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Cabannes, Eur. J. Mech. B/Fluids, 16, 1–15 (1997).

    MathSciNet  MATH  Google Scholar 

  8. O. Lindblom and N. Euler, Theor. Math. Phys., 131, 595–608 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Bobylev and G. Toscani, Contin. Mech. Thermodyn., 8, 257–274 (1996).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. V. Aristov and O. Ilyin, Phys. Lett. A, 374, 4381–4384 (2010).

    Article  ADS  Google Scholar 

  11. V. V. Aristov, Comput. Math. Math. Phys., 44, 1069–1081 (2004).

    MathSciNet  Google Scholar 

  12. F. Golse, Commun. Partial Differ. Equations, 12, 315–326 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  13. C. Cercignani, R. Illner, and M. Shinbrot, Commun. Math. Phys., 114, 687–698 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. M. Kogan, Dynamics of a Dilute Gas [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  15. V. Aristov, Phys. Lett. A, 250, 354–359 (1998).

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Dorodnitsyn Computation Center, RAS, Moscow, Russia

    O. V. Ilyin

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  1. O. V. Ilyin
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Correspondence to O. V. Ilyin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 170, No. 3, pp. 481–488, March, 2012.

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Ilyin, O.V. Stationary solutions of the kinetic Broadwell model. Theor Math Phys 170, 406–412 (2012). https://doi.org/10.1007/s11232-012-0039-0

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  • DOI: https://doi.org/10.1007/s11232-012-0039-0

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