Integral Conditions for Convergence of Solutions of Non-Linear Robin's Problem in Strongly Perforated Domain
DOI:
https://doi.org/10.15407/mag13.03.283Анотація
Розглядається початково-крайова задача для рiвняння Пуассона у сильно перфорованому середовищi Ωε = Ω\Fε ⊂ Rn (n ≥ 2) з нелiнiйною умовою Робiна на межi множини Fε, що перфорує. Область Ωε залежить вiд малого параметру ε > 0 так, що при ε→0 вона стає все бiльш розпушеною та розташовується все бiльш щiльно в областi Ω. Вивчається асимптотична поведiнка розв'язку задачi, коли ε→0. Побудовано усереднене рiвняння, що описує головний член u(x) асимптотики uε(x), та сформульованi iнтегральнi умови збiжностi uε(x) до u(x).
Mathematics Subject Classification: 35Q70.
Ключові слова:
усереднення, стаціонарна дифузія, нелінійна крайова умова Робіна, усереднене рівнянняПосилання
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