Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition
type: Item
instance of: scholarly article
title: Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition
zbMATH Open document ID: 1021.35009
DOI: 10.1007/BF02829795
author: Yanyan Li
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2003-10-21T00:00:00Z
review text: This paper is devoted to the homogenization of the family of parabolic equations over periodically perforated domains \[ \begin{cases} \partial_tb\left(\frac{x}{d_\varepsilon},u_\varepsilon\right)-\text{div }a(u_\varepsilon,\nabla u_\varepsilon)=f(x,t) & \text{in }\Omega_\varepsilon\times (0,T),\\ u_\varepsilon=0 & \text{on }\partial\Omega_\varepsilon\times(0,T),\\ u_\varepsilon(x,0)=u_0(x) & \text{in }\Omega_\varepsilon,\end{cases} \tag{\(1_\varepsilon\)} \] where \(\Omega_\varepsilon=\Omega\setminus S_\varepsilon\) is a periodically perforated domain and \(d_\varepsilon\) is a sequence of positive numbers which goes to zero. The authors' goal is to study the limiting behaviour of solution \((1_\varepsilon)\) and to obtain the limiting equation satisfied by the limit.
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 1870285
zbMATH Keywords: limiting equation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02829795
OpenAlex ID: W4229769030
description: scientific article; zbMATH DE number 1870285