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Journal of Mathematical Sciences

, Volume 202, Issue 5, pp 735–768 | Cite as

On the Large-Time Behavior of Solutions to the Cauchy Problem for a 2-dimensional Discrete Kinetic Equation

  • E. V. Radkevich
Article

Abstract

Existence of global solution for a 2-dimensional discrete equation of kinetics and expansion with respect to smoothness are obtained, and the effect of progressing waves generated by the operator of interaction is investigated.

Keywords

Cauchy Problem Global Solution Hardy Space Small Neighborhood Fourier Multiplier 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. V. Babin, A. A. Ilyin, and E. S. Titi, “On the regularization mechanism for the periodic KdV equation,” Commun. Pure Appl. Math., 64, 0591–0648 (2011).MathSciNetCrossRefGoogle Scholar
  2. 2.
    L. Boltzmann, “On the Maxwell method to the reduction of hydrodynamic equations from the kinetic gas theory,” Rep. Brit. Assoc., in the L. Boltzmann Memories, 2, 307–321, Nauka, Moscow (1984).Google Scholar
  3. 3.
    T. E. Broadwell, “Study of rarified shear flow by the discrete velocity method,” J. Fluid Mech., 19, No. 3 (1964).Google Scholar
  4. 4.
    S. Chapman and T. Cowling, Mathematical Theory of Nonuniform Gases, Cambridge University Press, Cambridge (1970).Google Scholar
  5. 5.
    G.Q. Chen, C.D. Levermore, and T.-P. Lui, “Hyperbolic conservation laws with stiff relaxation terms and entropy,” Commun. Pure Appl. Math., 47, No. 6, 787–830 (1994).CrossRefMATHGoogle Scholar
  6. 6.
    S. K. Godunov and U.M. Sultangazin, “On discrete models of the kinetic Boltzmann equation,” Russ. Math. Surv., 26, No. 3, 1–56 (1971).MathSciNetCrossRefGoogle Scholar
  7. 7.
    V. V. Palin and E.V. Radkevich, “Mathematical aspects of the Maxwell problem,” Appl. Anal., 88, No. 8, 1233–1264 (2009).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    E. V. Radkevich, Mathematical Aspects of Nonequilibrium Processes [in Russian], Izd. Tamary Rozhkovskoy, Novosibirsk (2007).Google Scholar
  9. 9.
    E.V. Radkevich, “The existence of global solutions to the Cauchy problem for discrete kinetic equations,” J. Math. Sci. (N.Y.) 181, No. 2, 232–280 (2012).MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    E.V. Radkevich, “The existence of global solutions to the Cauchy problem for discrete kinetic equations. II,” J. Math. Sci. (N.Y.), 181, No. 5, 701–750 (2012).MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    E.V. Radkevich, “On the nature of nonexistence of dissipative estimate for discrete kinetic equations,” Probl. Mat. Anal. 69, to be pubblished (2013).Google Scholar
  12. 12.
    V. V. Vedenyapin, Boltzmann and Vlasov Kinetic Equations [in Russian], Fizmatlit, Moscow (2001).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.M. V. Lomonosov Moscow State University, Faculty of Mechanics and MathematicsMoscowRussia

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