Skip to main content
SpringerLink
Log in

Self-similar solutions of the Laplacian growth problem in the half-plane

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We investigate a version of the Laplacian growth problem with zero surface tension in the upper half-plane. Using the method of time-dependent conformal maps, we find families of self-similar exact solutions that are expressible in terms of the hypergeometric function.

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

References

  1. A. Zabrodin, J. Phys. A, 42, 085206 (2009); arXiv:0811.4054v2 [math-ph] (2008).

    Article  MathSciNet  ADS  Google Scholar 

  2. S. D. Howison, European J. Appl. Math., 3, 209–224 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  3. P. J. Davis, The Schwarz Function and Its Applications (Carus Math. Monogr., Vol. 17), Math. Assoc. Amer., Buffalo, N.Y. (1974).

    MATH  Google Scholar 

  4. H. Thomé, M. Rabaud, V. Hakim, and Y. Couder, Phys. Fluids A, 1, 224–240 (1989).

    Article  ADS  Google Scholar 

  5. M. Ben Amar, Phys. Rev. A, 43, 5724–5727 (1991); 44, 3673–3685 (1991).

    Article  ADS  Google Scholar 

  6. Y. Tu, Phys. Rev. A, 44, 1203–1210 (1991).

    Article  ADS  Google Scholar 

  7. R. Combescot, Phys. Rev. A, 45, 873–884 (1992).

    Article  ADS  Google Scholar 

  8. I. Markina and A. Vasil’ev, Sci. Ser. A, 9, 33–43 (2003); European J. Appl. Math., 15, 781–789 (2004).

    MATH  MathSciNet  Google Scholar 

  9. A. Abanov, M. Mineev-Weinstein, and A. Zabrodin, Phys. D, 235, 62–71 (2007); arXiv:nlin.SI/0606068v2 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  10. A. I. Markushevich, Theory of Analytic Functions [in Russian], Vol. 2, Further Construction of the Theory, Nauka, Moscow (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics, Moscow, Russia

    D. V. Vasiliev & A. V. Zabrodin

  2. Emanuel Institute of Biochemical Physics, RAS, Moscow, Russia

    A. V. Zabrodin

Authors
  1. D. V. Vasiliev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Zabrodin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Zabrodin.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 166, No. 1, pp. 28–43, January, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vasiliev, D.V., Zabrodin, A.V. Self-similar solutions of the Laplacian growth problem in the half-plane. Theor Math Phys 166, 23–36 (2011). https://doi.org/10.1007/s11232-011-0002-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-011-0002-5

Keywords

Search

Navigation