Skip to main content
SpringerLink
Log in

Symmetrization and initial boundary-value problems for certain classes of nonlinear second order parabolic equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Initial boundary-value problems are considered for equations of porous medium andp-Laplace types. By using the Schwarz symmetrization method, theL p-estimates for the solutions of the original problems are obtained in terms of the analogous estimates for the corresponding symmetric solutions.

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. G. Talenti, “Elliptic equations and rearrangements,”Ann. Scuola Norm. Super. Piza. Sci. Fis. Mat.,4, No. 3, 697–718 (1976).

    Google Scholar 

  2. G. Talenti, “Linear Elliptic P. D. E's: Level sets, rearrangements and a priori estimates of solutions,”Boll. Unione Mat. Ital.,4B, No. 3, 917–949 (1985).

    Google Scholar 

  3. A. Alvino, G. Trombetti, and P.-L. Lions, “Comparison results for elliptic and parabolic equations via Schwarz symmetrization,”Ann. Inst. Henri. Poincaré,7, No. 2, 37–65 (1990).

    Google Scholar 

  4. E. Giarrusso, “Su una classe di equazioni non lineari elliptiche,”Ric. Mat.,31, No. 2, 245–257 (1982).

    Google Scholar 

  5. J. Vasquez, “Symmetrization in nonlinear parabolic equations,”Port. Math.,41, No. 1–4, 339–346 (1982).

    Google Scholar 

  6. J. Mossino and J. Rakotoson, “Isoperimetric inequalities in parabolic equations,”Ann. Scuola Norm. Super. Piza. Sci. Fis. Mat.,13, No. 1, 51–73 (1986).

    Google Scholar 

  7. M. Nakao, “Existence and decay of global solutions of some nonlinear degenerate parabolic equations,”J. Math. Anal. Appl.,109, 118–129 (1985).

    Google Scholar 

  8. 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 

  9. G. Hardy, J. Littlewood, and G. Polya,Inequalities [Russian translation], Izd. Inostr. Lit., Moscow (1948).

    Google Scholar 

  10. A. Alvino and G. Trombetti, “Su una classe di equazioni ellittiche non lineari degenery,”Ric. Mat.,29, No. 2, 193–212 (1980).

    Google Scholar 

  11. A. I. Nazarov and N. N. Ural'tseva, “Convex monotone hulls and the estimate of the maximum of a solution to a parabolic equation,” in:Boundary-Value Problems in Mathematical Physics and Related Problems in the Theory of Functions [in Russian], Issue 147, (1985) pp. 95–109.

Download references

Author information

Authors and Affiliations

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

    B. V. Bazalii & A. F. Tedeev

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. 45, No. 7, pp. 884–892, July, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bazalii, B.V., Tedeev, A.F. Symmetrization and initial boundary-value problems for certain classes of nonlinear second order parabolic equations. Ukr Math J 45, 976–986 (1993). https://doi.org/10.1007/BF01057444

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01057444

Keywords

Search

Navigation