Skip to main content
Log in

On the application of the principle of averaging for the solution of some parabolic boundary value problems

  • Published:
Ukrainian Mathematical Journal Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. Yu. A. Mitropol'skii, The Method of Averaging in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).

    Google Scholar 

  2. R. Z. Khas'minskii, “On the principle of averaging for parabolic and elliptic differential equations and Markov processes with small diffusion,” Probability Theory and Its Applications,8, No. 1 (1963).

  3. I. B. Simonenko, “The basis of the method of averaging for abstract parabolic equations,” Matem. Sb.,81 (123), No.l (1970).

  4. S. D. Éidel'man, “On the application of the principle of averaging to quasilinear parabolic systems of the second order,” Sib. Matem. Zh.,3, No.2 (1962).

  5. 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 

  6. V. P. Lavrenchuk and S.D. Ivasishen, “On the local solvability and continuation of the solutions of boundary value problems for quasilinear parabolic systems,” AN URSR, Ser. A, No. 10 (1969).

  7. S. D. Éidel'man and S. D. Ivasishen, “The investigation of the Green's matrix of a homogeneous parabolic boundary-value problem,” Tr. Mosk. Matem. Ob.,23 (1970).

  8. A. Fridman, Partial Differential Equations of Parabolic Type (Russian translation], Mir, Moscow (1968).

    Google Scholar 

  9. A.M. Il'in, A. S. Kalashnikov, and O. A. Oleinik, “Linear second order equations of parabolic type,” Usp. Matem. Nauk,17, No.3 (1962).

  10. I. I. Gikhman, “On a Theorem of Bogolyubov,” Ukr. Matem. Zh.,4, No.2 (1952).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol.25, No. 5, pp. 621–631, September–October, 1973.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Éidel'man, S.D., Sirchenko, Z.F. On the application of the principle of averaging for the solution of some parabolic boundary value problems. Ukr Math J 25, 516–524 (1973). https://doi.org/10.1007/BF01091944

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01091944

Keywords

Navigation