Advertisement

Doklady Mathematics

, Volume 98, Issue 3, pp 579–581 | Cite as

Uniqueness of Solution to the First Initial Boundary Value Problem for Parabolic Systems on the Plane in a Model Case

  • E. A. BaderkoEmail author
  • M. F. Cherepova
Mathematics
  • 2 Downloads

Abstract

The first initial boundary value problem for a one-dimensional (in x) Petrovskii parabolic second-order system with constant coefficients in a semibounded (in x) domain with a nonsmooth lateral boundary is proved to have a unique classical solution in certain Hölder classes.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. G. Petrovskii, Byul. Mosk. Gos. Univ. Sekts. A 1 (7), 1–72 (1938).Google Scholar
  2. 2.
    E. A. Baderko and M. F. Cherepova, Dokl. Math. 90 (2), 573–575 (2014).MathSciNetCrossRefGoogle Scholar
  3. 3.
    E. A. Baderko and M. F. Cherepova, Differ. Equations 52 (2), 197–209 (2016).MathSciNetCrossRefGoogle Scholar
  4. 4.
    E. A. Baderko and M. F. Cherepova, Dokl. Math. 96 (2), 423–426 (2017).MathSciNetCrossRefGoogle Scholar
  5. 5.
    V. G. Maz’ya and G. I. Kresin, Math. USSR Sb. 53 (2), 457–479 (1986).CrossRefGoogle Scholar
  6. 6.
    V. A. Solonnikov, Proc. Steklov Inst. Math. 83, 1–184 (1965).Google Scholar
  7. 7.
    O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’-tseva, Linear and Quasilinear Equations of Parabolic Type (Nauka, Moscow, 1967; Am. Math. Soc., Providence, R.I., 1968).CrossRefGoogle Scholar
  8. 8.
    A. Friedman, Partial Differential Equations of Parabolic Type (Prentice Hall, Englewood Cliffs, N.J., 1964).zbMATHGoogle Scholar
  9. 9.
    S. D. Eidel’man, Parabolic Systems (Nauka, Moscow, 1964) [in Russian].zbMATHGoogle Scholar
  10. 10.
    M. F. Cherepova, Vestn. Mosk. Energ. Inst., No. 6, 86–97 (1999).Google Scholar
  11. 11.
    M. F. Cherepova, Differ. Equations 36 (3), 457–465 (2000).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.National Research University “Moscow Power Engineering Institute” (MPEI)MoscowRussia

Personalised recommendations