Skip to main content
SpringerLink
Log in

Analyticity of a free boundary in one problem of axisymmetric flow

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We prove the solvability of a boundary-value problem in the case where the Bernoulli condition is given on a free boundary in the form of an inequality. We establish the analyticity of the free boundary.

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

References

  1. A. S. Minenko, “On one thermal problem with free boundary,” Dokl. Akad. Nauk Ukr. SSR, No. 6, 413–416 (1979).

  2. I. I. Danilyuk and A. S. Minenko, “On the variational method for investigation of the quasistationary Stefan problem,” Usp. Mat. Nauk, 43, No. 5, 228 (1981).

    Google Scholar 

  3. A. S. Minenko, “Analyticity of the free boundary in one thermal problem,” Mat. Fizika, Issue 33, 80–82 (1983).

    Google Scholar 

  4. I. I. Danilyuk and A. S. Minenko, “One variational problem with free boundary,” in: Proc. of the Conf. on Mixed Boundary-Value Problems for Partial Differential Equations and Problems with Free Boundaries, Stuttgart (1978), pp. 9–18.

  5. A. S. Minenko, “Axisymmetric flow with free boundary,” Ukr. Mat. Zh., 47, No. 4, 477–488 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  6. I. I. Danilyuk, “Integral functionals with varying domain of integration,” Tr. Mat. Inst. Akad. Nauk SSSR, 118, 1–112 (1972).

    MathSciNet  Google Scholar 

  7. D. Kinderlehrer and L. Nirenberg, “Regularity in free boundary problems,” Ann. Scuola Norm. Super. Pisa. Ser 4, 4, 373–391 (1977).

    MATH  MathSciNet  Google Scholar 

  8. C. Baiocchi, “Sur une problème á frontiére libre traduisant le filtrage de liquides á traverse des milieux poreux,” C. r. Acad. Sci. A, 273, 1215–1217, (1971).

    MATH  MathSciNet  Google Scholar 

  9. H. W. Alt and L. A. Caffarelli, “Existence and regularity for a minimum problem with free boundary,” J. Math., 325, 107–144, (1980).

    Google Scholar 

  10. A. Friedman, “Axially symmetric cavities in flows,” Commun. Partial Different. Equat., 8, No. 9, 949–997, (1983).

    Article  MATH  Google Scholar 

  11. P. R. Garabedian, H. Lewy, and M. Schiffer, “Axially symmetric cavitational flow,” Ann. Math., 56, No. 3, 560–602, (1952).

    Article  MathSciNet  Google Scholar 

  12. M. A. Evgrafov, Analytic Functions [in Russian], Nauka, Moscow (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Problems of Artificial Intellect, Ukrainian Academy of Sciences, Donetsk

    A. S. Minenko

Authors
  1. A. S. Minenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1692–1700, December, 1998.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Minenko, A.S. Analyticity of a free boundary in one problem of axisymmetric flow. Ukr Math J 50, 1929–1938 (1998). https://doi.org/10.1007/BF02514209

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02514209

Keywords

Search

Navigation