Homogenization of the variational inequality corresponding to a problem with rapidly varying boundary conditions
type: Item
instance of: scholarly article
title: Homogenization of the variational inequality corresponding to a problem with rapidly varying boundary conditions
zbMATH Open document ID: 1157.35010
DOI: 10.1134/S0001434607090246
author: M. N. Zubova
author: T. A. Shaposhnikova
published in: Mathematical Notes
publication date: 2008-09-03T00:00:00Z
review text: The authors investigate the asymptotic behavior of a solution \(\;u_\varepsilon\in K_\varepsilon\) of a variational inequality \[ \int_\Omega \nabla u_\varepsilon\cdot \nabla(v-u_\varepsilon)dx\geq \int_\Omega f(v-u_\varepsilon)dx\;\forall v\in K_\varepsilon, \] where \newline \(K_\varepsilon=\{g\in H_1(\Omega,\Gamma_2):g\geq 0\;\text{ on}\;G_\varepsilon\}\;\) with \(\varepsilon\)-periodically located subsets \(G_\varepsilon\) belonging to the boundary \(\partial\Omega\) of the domain \(\Omega \subset \{x\in \mathbb{R}^3:x_1>0\}.\;\) They construct a limit (homogenized) problem and prove the strong in \(H_1(\Omega)\) convergence of the solutions of the original variational inequality to the solution of the limit nonlinear boundary-value problem as \(\varepsilon\rightarrow 0\) in the so-called critical state.
reviewed by: Igor Bock
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35J85
zbMATH DE Number: 5319862
zbMATH Keywords: variational inequality
zbMATH Keywords: rapidly varying boundary conditions
zbMATH Keywords: boundary homogenization
zbMATH Keywords: strong convergence
zbMATH Keywords: domain with periodically bounded subsets
MaRDI profile type: Publication
cites work: Boundary homogenization for elliptic problems
cites work: AVERAGING OF BOUNDARY VALUE PROBLEMS WITH A SINGULAR PERTURBATION OF THE BOUNDARY CONDITIONS
cites work: Boundary value problem for the Laplacian with rapidly oscillating boundary conditions
cites work: Q4469375
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full work available at URL: s0001434607090246
OpenAlex ID: W1998925518
description: scientific article; zbMATH DE number 5319862