Skip to main content
SpringerLink
Log in

Estimates of the rate of stabilization of certain problems with free boundary

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

With the help of energy estimates we study the behavior of solutions of the Dirichlet problem and the Stefan problem under unbounded growth of time for the semilinear equation ut − uXX + uβ = 0, β ∈ (0, 1), in the case of one geometric variable.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. A. A. Samarskii, V. A. Galaktinov, S. P. Kurdyumov, and A. P. Mikhailov, Peaking Modes in Problems for Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  2. B. V. Bazalii and V. Yu. Shelepov, “On the stabilization of the solution of the Stefan problem for a certain quasilinear equation,” in: Boundary-Value Problems of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1979); pp. 24–39.

    Google Scholar 

  3. A. Friedman, “The Stefan problem in several space variables,” Trans. Amer. Math. Soc.,132, 51–87 (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Academy of Sciences of the Ukraine, Donetsk

    B. V. Bazalii (Doctor of Physicomathematical Sciences) & A. F. Tedeev (Candidate of Physicomathematical Sciences)

Authors
  1. B. V. Bazalii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. F. Tedeev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1299–1306, October, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bazalii, B.V., Tedeev, A.F. Estimates of the rate of stabilization of certain problems with free boundary. Ukr Math J 44, 1189–1196 (1992). https://doi.org/10.1007/BF01057673

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01057673

Keywords

Search

Navigation