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Nonlinear parabolic problems in perforated domains

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Abstract

The behavior of the remainder term of the asymptotic expansion for solutions of a quasi-linear parabolic Cauchy-Dirichlet problem in a sequence of domains with fine-granulated boundary is studied. By using a modification of the asymptotic expansion and new pointwise estimates of solutions of the model problem, the uniform convergence of the remainder term to zero is proved.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences, Kiev, Ukraine

    A. V. Zhuravskaya

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  1. A. V. Zhuravskaya
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Correspondence to A. V. Zhuravskaya.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 53, Suzdal Conference-2006, Part 1, 2008.

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Zhuravskaya, A.V. Nonlinear parabolic problems in perforated domains. J Math Sci 157, 491–495 (2009). https://doi.org/10.1007/s10958-009-9329-y

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  • DOI: https://doi.org/10.1007/s10958-009-9329-y

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