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Homogenization of boundary value problems in perforated domains with the third boundary condition and the resulting change in the character of the nonlinearity in the problem

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Abstract

We study the homogenization problem for the Poisson equation in a periodically perforated domain with a nonlinear boundary condition for the flux on the cavity boundaries. We show that, under certain relations on the problem scale, the homogenized equations may have different character of the nonlinearity. In each case considered, we obtain estimates for the convergence of solutions of the original problem to the solution of the homogenized problem in the corresponding Sobolev spaces.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    M. N. Zubova & T. A. Shaposhnikova

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  1. M. N. Zubova
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  2. T. A. Shaposhnikova
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Original Russian Text © M.N. Zubova, T.A. Shaposhnikova, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 1, pp. 79–91.

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Zubova, M.N., Shaposhnikova, T.A. Homogenization of boundary value problems in perforated domains with the third boundary condition and the resulting change in the character of the nonlinearity in the problem. Diff Equat 47, 78–90 (2011). https://doi.org/10.1134/S0012266111010095

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  • DOI: https://doi.org/10.1134/S0012266111010095

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