Ukrainian Mathematical Journal

, Volume 59, Issue 1, pp 111–125 | Cite as

Nonlocal Dirichlet problem for linear parabolic equations with degeneration

  • I. D. Pukal’s’kyi


In the spaces of classical functions with power weight, we prove the correct solvability of the Dirichlet problem for parabolic equations with nonlocal integral condition with respect to the time variable and an arbitrary power order of degeneration of coefficients with respect to the time and space variables.


Parabolic Equation Dirichlet Problem Nonlocal Condition Interpolation Inequality Power Weight 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. I. Kamyshin and B. N. Khimchenko, “A priori estimates for a solution of the parabolic equation of the second order near the lower cap of the parabolic limit,” Sib. Mat. Zh., 22, No. 4, 94–113 (1981).Google Scholar
  2. 2.
    L. I. Kamyshin and B. N. Khimchenko, “On maximum principle for an elliptic-parabolic equation of the second order,” Sib. Mat. Zh., 13, No. 4, 777–789 (1972).Google Scholar
  3. 3.
    M. I. Matiichuk, Parabolic Singular Boundary-Value Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (1999).Google Scholar
  4. 4.
    A. V. Babin and S. Zh. Kabakbaev, “On the smoothness up to the boundary of solutions of parabolic equations with degenerate operator,” Mat. Sb., 185, No. 7, 13–38 (1994).zbMATHGoogle Scholar
  5. 5.
    V. M. Borok and M. A. Perel’man, “On classes of uniqueness of a solution of the multipoint boundary-value problem in an infinite layer,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 8, 29–34 (1973).Google Scholar
  6. 6.
    I. D. Pukal’skyi, “Nonlocal Neumann problem for the parabolic equation with degenerations,” Ukr. Mat. Zh., 51, No. 9, 1232–1244 (1999).CrossRefGoogle Scholar
  7. 7.
    I. D. Pukal’s’kyi, “One-sided nonlocal boundary-value problem for singular parabolic equations,” Ukr. Mat. Zh., 53, No. 11, 1521–1531 (2001).Google Scholar
  8. 8.
    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
  9. 9.
    S. D. Éidel’man, Parabolic Systems [in Russian], Nauka, Moscow (1964).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • I. D. Pukal’s’kyi
    • 1
  1. 1.Chernivtsi National UniversityChernivtsi

Personalised recommendations