Homogenization of the boundary value problem for the poisson equation with rapidly oscillating nonlinear boundary conditions: space dimension n ≥ 3, critical case
- Authors: Podolskiy A.V.1, Shaposhnikova T.A.1
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Affiliations:
- Moscow State University
- Issue: Vol 485, No 3 (2019)
- Pages: 263-268
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12828
- DOI: https://doi.org/10.31857/S0869-56524853263-268
- ID: 12828
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Abstract
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
About the authors
A. V. Podolskiy
Moscow State University
Email: shaposh.tan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
T. A. Shaposhnikova
Moscow State University
Author for correspondence.
Email: shaposh.tan@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
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