Averaging of boundary-value problems for the Laplace operator in perforated domains with a nonlinear boundary condition of the third type on the boundary of cavities |
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Authors: | M. N. Zubova T. A. Shaposhnikova |
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Affiliation: | 1. Moscow State University, Moscow, Russia
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Abstract: | In this paper, the asymptotic behavior of solutions u ε of the Poisson equation in the ε-periodically perforated domain Ωε ? $ {{mathbb{R}}^n} $ , n ≥ 3, with the third nonlinear boundary condition of the form ? ν u ε + ε?γσ(x, u ε) = ε ?γ g(x) on a boundary of cavities, is studied. It is supposed that the diameter of cavities has the order εα with α > 1 and any γ. Here, all types of asymptotic behavior of solutions u ε , corresponding to different relations between parameters α and γ, are studied. |
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