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Mathematical Notes

, Volume 77, Issue 5–6, pp 708–714 | Cite as

Cauchy Problem for a System of Equations of Ultraparabolic Type

  • S. A. Tersenov
Article
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Abstract

This paper is devoted to the proof of the existence of a solution of the Cauchy problem for a system of equations of ultraparabolic type.

Key words

system of equations of ultraparabolic type Cauchy problem simply connected surface parabolic system in the sense of Petrovskii 

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REFERENCES

  1. 1.
    S. A. Tersenov, “On the main boundary-value problems for a certain ultraparabolic equation,” Sibirsk. Mat. Zh. [Siberian Math. J.], 40 (1999), no. 6, 1364–1376.Google Scholar
  2. 2.
    N. S. Genchev, “On ultraparabolic equations,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 151 (1963), no. 2, 205–268.Google Scholar
  3. 3.
    V. S. Vladimirov and Yu. N. Drozhzhinov, “A generalized Cauchy problem for ultraparabolic equations,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 31 (1967), no. 6, 1341–1360.Google Scholar
  4. 4.
    O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow, 1967.Google Scholar
  5. 5.
    Sh. Amirov, “A mixed problem for ultraparabolic equations in bounded domains,” in: Well-Posed Boundary-Value Problems for Nonclassical Equations of Mathematical Physics [in Russian] Institute of Mathematics, Siberian Division of the Academy of Sciences of the USSR, Novosibirsk, 1984.Google Scholar
  6. 6.
    L. G. Gomboev, “On a well-posed problem for an equation of ultraparabolic type,” in: Problems of Differential Equations and Discrete Mathematics [in Russian], Novosibirsk State University, Novosibirsk, 1986, pp. 44–51.Google Scholar
  7. 7.
    S. G. Pyatkov, “Solvability of boundary-value problems for ultraparabolic equations,” in: Nonclassical Equations and Equations of Mixed Type [in Russian], Institute of Mathematics, Siberian Division of the Academy of Sciences of the USSR, Novosibirsk, 1990, pp. 182–197.Google Scholar
  8. 8.
    Ya. I. Shatyro, “The first boundary-value problem for a particular ultraparabolic equation,” Differentsial’nye Uravneniya [Differential Equations] (1971), no. 7, 1089–1141.Google Scholar
  9. 9.
    A. S. Tersenov, “A priori estimates for a class of degenerate parabolic and ultraparabolic equations,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 338 (1994), no. 2, 168–170.Google Scholar
  10. 10.
    M. Manfredini, “The Dirichlet problem for a class of ultraparabolic equations,” Adv. Differential Equations, 2 (1997), no. 5, 831–866.Google Scholar
  11. 11.
    S. Polidoro, “On a class of ultraparabolic operators of Kolmogorov-Fokker-Planck type,” Matematiche (Catania), 49 (1994), no. 1, 53–105.Google Scholar
  12. 12.
    A. M. Il’in, “On a class of ultraparabolic equations,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 159 (1964), no. 6, 1214–1217.Google Scholar
  13. 13.
    G. Hr. Kirov, “The Dirichlet problem for a certain ultraparabolic equation,” Godisnik Viss. Tehn. Ucebn. Zaved. Mat., 6 (1970), no. 2, 101–118.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. A. Tersenov
    • 1
  1. 1.S. L. Sobolev Institute of Mathematics, Siberian DivisionRussian Academy of SciencesNovosibirskRussia

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