Open AccessHomogenization of the boundary value problem for the poisson equation with rapidly oscillating nonlinear boundary conditions: space dimension n ≥ 3, critical case
Author(s) -
Alexander Podolskiy,
Т. А. Шапошникова
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524853263-268
Subject(s) - homogenization (climate) , robin boundary condition , mathematics , mathematical analysis , neumann boundary condition , boundary value problem , mixed boundary condition , bounded function , nonlinear system , cauchy boundary condition , poisson's equation , boundary values , physics , biodiversity , ecology , quantum mechanics , biology
The homogenization of the Poisson equation in a bounded domain with rapidly oscillating boundary conditions specied on a part of the domain boundary is studied. A Neumann boundary condition alternates with an ε-periodically distributed nonlinear Robin condition involving the coefficient ε-β, where β ∈ R. The diameter of the boundary portions with a nonlinear Robin condition is of order O(εα), α > 1. A critical relation between the parameters α and β is considered