Asymptotic expansion of solutions of quasilinear parabolic problems in perforated domains
type: Item
instance of: scholarly article
title: Asymptotic expansion of solutions of quasilinear parabolic problems in perforated domains
zbMATH Open document ID: 0869.35014
DOI: 10.1007/BF01060863
published in: Ukrainian Mathematical Journal
publication date: 1996-10-30T00:00:00Z
review text: The author deals with an averaging of the solution of the initial-boundary value problem for a quasilinear parabolic equation in a perforated domain, assuming that the diameters of perforations tend to zero (and the number of perforations eventually tends to infinity). Under some condition on the coefficients, a priori estimates are obtained and the weak convergence of the solutions in the space \(W^{1,1/2}_2\) is proved. After formulation of some local (or model) problems the series of correctors in the form of an asymptotic expansion is constructed. The main result is a theorem about strong convergence of the remainders of this expansion to zero in the space \(W^{1,1/2}_2\). Note that, because of very general assumptions about the sequence of domains, the weak limit of solutions is not identified. However, it is important to point out that the convergence result is obtained without additional assumption about the distribution of perforations.
reviewed by: Ibrahim Aganović
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 923084
zbMATH Keywords: fine-grained boundary
zbMATH Keywords: averaging
zbMATH Keywords: quasilinear parabolic equation
author: Igor V. Skrypnik
MaRDI profile type: Publication
cites work: Q5548525
cites work: Q4726666
cites work: Q3992466
cites work: Q3344554
description: scientific article; zbMATH DE number 923084