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.
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References
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).
F. Bernis,Qualitative Properties for Some Nonlinear Higher Degenerate Parabolic Equations, IMA. Preprint No. 184, University of Minnesota (1985).
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).
S. N. Antontsev, “On localization of solutions of nonlinear degenerating elliptic and parabolic equations,”Dokl. Akad. Nauk SSSR,260, No. 6, 1289–1293 (1981).
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).
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).
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).
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).
A. F. Tedeev, “On multiplicative inequalities in regions with a noncompact boundary,”Ukr. Mat. Zh.,44, No. 2, 260–268 (1992).
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).
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).
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).
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Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 11, pp. 1571–1579, November, 1993.
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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
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DOI: https://doi.org/10.1007/BF01060865