Skip to main content
Log in

Instantaneous appearance of singularities of a solution of a degenerate parabolic equation

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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. J. I. Diaz and R. Kersner, “On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium,” Math. Res. Center, Univ. Wisconsin, Madison, Techn. Summary Report, N2502, 1983.

    Google Scholar 

  2. J. I. Diaz and R. Kersner, “Nonexistence of one of the free boundaries in a degenerated equation in filtration theory,” C. R. Acad. Sci.,296, Ser. 1, 505–508 (1983).

    Google Scholar 

  3. A. S. Kalashnikov, “Appearance of singularities in a solution of a nonstationary filtration equation,” Zh. Vychisl. Mat. Mat. Fiz.,7, No. 2, 440–444 (1967).

    Google Scholar 

  4. B. Knerr, “The porous medium equation in one dimension,” Trans. Am. Math. Soc.,234, No. 2, 381–415 (1977).

    Google Scholar 

  5. V. I. Nalimov and V. V. Pukhnachev, Instability of Motion of an Ideal Fluid with Free Boundary [in Russian], Novosibirsk State Univ. (1975).

  6. 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 

  7. S. N. Kruzhkov, “Nonlinear parabolic equations with two independent variables,” Tr. Mosk. Mat. Obshch.,16, 329–346 (1967).

    Google Scholar 

  8. A. S. Kronrod and E. M. Landis, “Level sets of functions of several variables,” Dokl. Akad. Nauk SSSR,58, No. 7, 1269–1272 (1947).

    Google Scholar 

Download references

Authors

Additional information

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 4, pp. 166–179, July–August, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shmarev, S.I. Instantaneous appearance of singularities of a solution of a degenerate parabolic equation. Sib Math J 31, 671–682 (1990). https://doi.org/10.1007/BF00970640

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970640

Keywords

Navigation