Skip to main content
SpringerLink
Log in

On Exact Solutions of Nonlinear Diffusion Equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

New classes of the exact solutions of nonlinear diffusion equations are constructed.

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.

Similar content being viewed by others

REFERENCES

  1. R. A. Fisher, “The wave of advance of advantageous genes,” Ann. Eugenics, 7, 353–369 (1937).

    Google Scholar 

  2. J. D. Marrey, Mathematical Biology, Springer, Berlin (1989).

    Google Scholar 

  3. M. I. Serov and R. M. Cherniha, “Lie symmetries and exact solutions of nonlinear heat equations with convection term,” Ukr. Mat. Zh., 49, No.9, 1262–1270 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Cherniha and M. Serov, “Lie and non-Lie symmetries of nonlinear diffusion equations with convection term,” i n: Proceedings of the Second International Conference “Symmetry in Nonlinear Mathematical Physics,” Vol. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (1997), pp. 444–449.

    Google Scholar 

  5. A. G. Nikitin and T. A. Barannyk, “Solitary wave and other solutions for nonlinear heat equations,” math-ph/0304004.

  6. V. I. Fushchich, V. M. Shtelen', and N. I. Serov, Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1989).

    MATH  Google Scholar 

  7. L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).

    MATH  Google Scholar 

  8. D. Levi and P. Winternitz, “Nonclassical symmetry reduction: example of the Boussinesq equation,” J. Phys. A: Math. Gen., 22, 2915–2924 (1989).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pomorska Akademia Pedagogiczna, Slupsk, Poland

    A. F. Barannyk

  2. National University of Food Technology, Kyiv, Ukraine

    I. I. Yuryk

Authors
  1. A. F. Barannyk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. I. Yuryk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1011 – 1019, August, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barannyk, A.F., Yuryk, I.I. On Exact Solutions of Nonlinear Diffusion Equations. Ukr Math J 57, 1189–1200 (2005). https://doi.org/10.1007/s11253-005-0256-x

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-005-0256-x

Keywords

Search

Navigation