The oscillating boundary phenomenon in the homogenization of a climatization problem
type: Item
instance of: scholarly article
title: The oscillating boundary phenomenon in the homogenization of a climatization problem
zbMATH Open document ID: 1017.35017
DOI: 10.1023/A:1012525913457
author: Svetlana E. Pastukhova
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: Let \(\Omega\subset\mathbb{R}^2\) be a bounded domain, \(\varepsilon>0\) a small parameter and \(\Omega_\varepsilon\) the domain obtained by \(\varepsilon\)-periodic perturbation \(\partial\Omega_\varepsilon\) (with the amplitude \(\varepsilon)\) of the boundary \(\partial\Omega\). The author considers a homogenization of the stationary heat conduction problem in \(\Omega_\varepsilon \), assuming that on \(\partial\Omega_\varepsilon\) the heat exchange is governed by the Newton's law, that the temperature never falls below some given level and that the heat flux is one-directional. The problem is formulated as a variational inequality; the existence and uniqueness of a solution is established. The homogenized problem is found out and the convergence of the homogenization process is proved. A similar problem was considered in the paper of \textit{W. Jäger}, \textit{O. A. Oleinik} and \textit{T. A. Shaposhnikova} [Differ. Equ. 36, 833-846 (2000; Zbl 0993.35013)].
reviewed by: Ibrahim Aganović
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 86A10
zbMATH DE Number: 1915932
zbMATH Keywords: oscillating boundary
zbMATH Keywords: heat conduction
zbMATH Keywords: homogenization
zbMATH Keywords: variational inequality
MaRDI profile type: Publication
full work available at URL: a:1012525913457
OpenAlex ID: W97632227
description: scientific article; zbMATH DE number 1915932