Skip to main content
Log in

Qualitative properties of solutions of the Neumann problem for a higher-order quasilinear parabolic equation

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

The property of localization of perturbations is proved for a solution of an initial boundary-value Neumann problem in a regionD=Ωx, t>0, where Ω is a region in Rnwith a noncompact boundary.

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.

Similar content being viewed by others

References

  1. A. K. Gushchin, “On estimates of solutions of boundary-value problems for a second-order parabolic equation,”Tr. Mat. Inst. Akad. Nauk SSSR,126, 5–45 (1973).

    Google Scholar 

  2. F. Bernis,Qualitative Properties for Some Nonlinear Higher Degenerate Parabolic Equations, IMA. Preprint No. 184, University of Minnesota (1985).

  3. F. Bernis, “Finite speed of propagation and asymptotic rates for some nonlinear higher-order parabolic equations with absorption,”Proc. Roy. Soc. Edinburgh A,104, 1–19 (1986).

    Google Scholar 

  4. S. N. Antontsev, “On localization of solutions of nonlinear degenerating elliptic and parabolic equations,”Dokl. Akad. Nauk SSSR,260, No. 6, 1289–1293 (1981).

    Google Scholar 

  5. T. L. Diaz and L. Veron, “Local vanishing properties of solutions of elliptic and parabolic quasilinear equations,”Trans. Am. Math. Soc.,290, No. 2, 787–814 (1985).

    Google Scholar 

  6. A. F. Tedeev, “Qualitative properties of a solution of the second mixed problem for a fourth-order parabolic quasilinear equation,” in:Abstracts of VII Republican Conference [in Russian], Donetsk (1991).

  7. G. Talenti, “Linear elliptic P. D. E's: Level sets, rearrangements, and a priori estimates of solutions,”Boll. Unione. Mat. Ital.,B4, No. 3, 918–949 (1985).

    Google Scholar 

  8. A. F. Tedeev, “Stabilization of a solution of the third mixed problem for second-order parabolic quasilinear equations in a noncylindrical domain,”Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 1, 63–73 (1991).

    Google Scholar 

  9. A. F. Tedeev, “On multiplicative inequalities in regions with a noncompact boundary,”Ukr. Mat. Zh.,44, No. 2, 260–268 (1992).

    Google Scholar 

  10. R. C. Brown and D. B. Hinton, “Weighted interpolation inequalities of sum and product form in Rn,”Proc. London Math. Soc.,56, No. 2, 261–280 (1988).

    Google Scholar 

  11. A. V. Glushak, M. Transirico, and M. Troisi, “Teoremi di immersione ed equazioni ellittiche in aperti non limitati,”Rend. Mat. Appl.,9, No. 1, 113–130 (1986).

    Google Scholar 

  12. A. F. Tedeev, “Estimates of the rate of stabilization of a solution to the second mixed problem for a second-order parabolic quasilinear equation ast → ∞,”Differents. Uravn.,27, No. 10, 1795–1806 (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 11, pp. 1571–1579, November, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tedeev, A.F. Qualitative properties of solutions of the Neumann problem for a higher-order quasilinear parabolic equation. Ukr Math J 45, 1767–1778 (1993). https://doi.org/10.1007/BF01060865

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01060865

Keywords

Navigation