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Differential Equations

, Volume 47, Issue 1, pp 78–90 | Cite as

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

  • M. N. Zubova
  • T. A. Shaposhnikova
Partial Differential Equations

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.

Keywords

Generalize Solution Poisson Equation Integral Identity Homogenization Problem Nonlinear Boundary Condition 
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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • M. N. Zubova
    • 1
  • T. A. Shaposhnikova
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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