Journal of Mathematical Sciences

, Volume 144, Issue 4, pp 4234–4240 | Cite as

On the properties of representation of the Fokker-Planck equation in the Hermite function basis

  • E. V. Radkevich


Cauchy Problem Asymptotic Stability Poisson Bracket Planck Equation Collision Operator 
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  1. 1.
    S. K. Godunov, Ordinary Differential Equations with Constant Coefficiennts [in Russian], Novosibirsk (1994).Google Scholar
  2. 2.
    H. Grad, “On the kinetic theory of rarefied gases,” Commun. Pure Math., 2 (1949).Google Scholar
  3. 3.
    C. Hermite, Oeuvres, Vol. I, Paris (1905), pp. 397–414.Google Scholar
  4. 4.
    C. D. Levermore, “Moment closure hierarchies for kinetic theories,” J. Stat. Phys., 83, 1021–1065 (1996).MATHCrossRefGoogle Scholar
  5. 5.
    Muller Ruggeri T. Extended Thermodynamics, Springer-Verlag (1993).Google Scholar
  6. 6.
    E. V. Radkevich, “Well-posedness of mathematical models in continuum mechanics and thermodynamics,” Contemp. Math. Fund. Directions, No. 3 (2003), pp. 1–32.Google Scholar
  7. 7.
    L. R. Vokevich and E. V. Radkevich, “Stable pencils of hyperbolic polynomials and asymptotic stability of the Cauchy problem for certain systems of non-equilibrium thermodynamics,” Tr. Mosk. Mat. Obshch., 65, 69–113 (2004).Google Scholar
  8. 8.
    L. R. Volevich and E. V. Radkevich, “Uniform estimates for solutions of the Cauchy problem for hyperbolic equations with a small parameter by higher derivatives,” Differ. Uravn., 39, No. 4, 1–14 (2003).Google Scholar
  9. 9.
    P. A. Zakharchenko and E. V. Radkevich, “On hyperbolic pencils of Grad moment systems of nonequilibrium thermodynamics,” Tr. Semin. Petrovskogo, 24, 67–94 (2004).Google Scholar
  10. 10.
    P. A. Zakharchenko and E. V. Radkevich, “On correctness of approximations of the Fokker-Planck equation by moment systems,” Dokl. Ross. Akad. Nauk, 397, No. 6, 762–766 (2004).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • E. V. Radkevich
    • 1
  1. 1.Moscow State UniversityRussia

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