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Asymptotic expansion of solutions of quasilinear parabolic problems in perforated domains

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Abstract

An asymptotic expansion is constructed for solutions of quasilinear parabolic problems with Dirichlet boundary conditions in domains with a fine-grained boundary. It is proved that the sequence of remainders of this expansion in the space W 1.1/22 strongly converges to zero.

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References

  1. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. M. Ural'tseva,Linear and Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  2. V. A. Marchenko and E. Ya. Khruslov,Boundary-Value Problems in Regions with Fine-Grained Boundaries [in Russian], Naukova Dumka, Kiev (1974).

    Google Scholar 

  3. I. V. Skrypnik,Nonlinear Elliptic Boundary-Value Problems, B. G. Teubner Verlagsgesellschaft, Leipzig (1986).

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  4. I. V. Skrypnik,Methods for Studying Nonlinear Elliptic Boundary-Value Problems [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  5. S. A. Lamonov, “On convergence of solutions of the first boundary-value problem for quasilinear parabolic equations in regions with fine-grained boundaries,”Mat. Fiz. Nelin. Mekh., Issue 2, 60–63 (1984).

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  6. I. V. Skrypnik, “Pointwise estimates of a solution of a model nonlinear parabolic problem,”Nelin. Granich. Zadachi, Issue 3, 72–86 (1991).

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Authors and Affiliations

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

    I. V. Skrypnik (Academician, Ukrainian Academy of Sciences)

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  1. I. V. Skrypnik
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1542–1566, November, 1993.

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Skrypnik, I.V. Asymptotic expansion of solutions of quasilinear parabolic problems in perforated domains. Ukr Math J 45, 1736–1761 (1993). https://doi.org/10.1007/BF01060863

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  • DOI: https://doi.org/10.1007/BF01060863

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