On homogenization of the mixed boundary value problem for the heat equation in a domain whose part contains channels arranged in a periodic way
type: Item
instance of: scholarly article
title: On homogenization of the mixed boundary value problem for the heat equation in a domain whose part contains channels arranged in a periodic way
zbMATH Open document ID: 0971.35012
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-11-13T00:00:00Z
review text: The asymptotic behaviour of solutions \(u_\varepsilon\) of an initial boundary value problem for the heat equation in a partially perforated domain \(\Omega_\varepsilon\) is studied. The domain \(\Omega_\varepsilon\) is of the form \(\Omega_\varepsilon= \Omega^-\cup \Omega_\varepsilon^+\cup\gamma\), where \(\Omega^-\), \(\Omega^+_\varepsilon\) are disjunct regular domains, having a contact hypersurface \(\gamma\) on the boundary; \(\Omega^+_\varepsilon\) is obtained by removing, from a domain \(\Omega\subset \mathbb{R}^n\), a collection of periodically distributed and identical obstacles of size \(\varepsilon\). The Neumann condition on boundaries of obstacles and the Dirichlet condition on the other part of \(\partial\Omega_\varepsilon\) is posed. The homogenized problem is the Dirichlet problem in the domain \(\Omega\cup\Omega^-\cup\gamma\), with the transmission conditions on \(\gamma\). The authors found out the estimates for the difference between \(u_\varepsilon\) and the solution of the homogenized problem.
reviewed by: Ibrahim Aganović
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 80M40
zbMATH DE Number: 1526522
zbMATH Keywords: initial boundary value problem
zbMATH Keywords: partially perforated domain
zbMATH Keywords: Neumann condition on boundaries of obstacles
zbMATH Keywords: Dirichlet condition on the other part
author: Olga Arsenevna Oleĭnik
author: T. A. Shaposhnikova
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1526522