Asymptotic behaviour of linear Dirichlet parabolic problems with variable operators depending on time in varying domains
type: Item
instance of: scholarly article
title: Asymptotic behaviour of linear Dirichlet parabolic problems with variable operators depending on time in varying domains
zbMATH Open document ID: 1072.35025
author: Carmen Calvo-Jurado
author: Juan Casado-Díaz
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-06-01T00:00:00Z
review text: The authors consider the initial value problem for a linear parabolic problem in which the coefficients and the domain vary simultaneosly and give a generalization to the parabolic case of the results given in elliptic case by \textit{G. Dal Maso, I. V. Skrypnik} [Potential Anal. 7, No. 4, 765--803 (1997; Zbl 0887.31005)]. Substantially the authors prove that in the limit problem the H-limit of the (elliptic part of the) operator appears as well as a ``strange term'' of order zero similar to the one which appears in the elliptic case. A corrector result is also obtained. The methods are different from the ones of Dal Maso-Murat and are more similar to the methods used by the authors in [Proc. R. Soc. Edinb., Sect. A, Math. 133, 1231--1248 (2003; Zbl 1052.35017)].
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 2173099
zbMATH Keywords: \(H\)-convergence
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.12.051
OpenAlex ID: W1986066869
cites work: Q4197852
cites work: Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations
cites work: The limit of Dirichlet systems for variable monotone operators in general perforated domains.
cites work: Homogenization of Dirichlet parabolic systems with variable monotone operators in general perforated domains
cites work: Homogenization of general quasi-linear Dirichlet problems with quadratic growth in perforated domains
cites work: Homogenisation of Dirichlet problems for monotone operators in varying domains
cites work: Homogenization of Dirichlet pseudomonotone problems with renormalized solutions in perforated domains
cites work: Q4946284
cites work: Asymptotic Behavior of Nonlinear Elliptic Systems on Varying Domains
cites work: Q3961204
cites work: NEW RESULTS ON THE ASYMPTOTIC BEHAVIOR OF DIRICHLET PROBLEMS IN PERFORATED DOMAINSDIRICHLET PROBLEMS IN PERFORATED DOMAINS
cites work: Wiener's criterion and \(\Gamma\)-convergence
cites work: Limits of nonlinear Dirichlet problems in varying domains
cites work: Q4371385
cites work: Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems
cites work: Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
cites work: Q3029673
cites work: Q5648620
cites work: An effect of double homogenization for Dirichlet problems in variable domains of general structure
cites work: Q5890172
cites work: Q5334555
cites work: Q4218870
cites work: Q4365247
cites work: SOME PROPERTIES OF THE SPECTRUM OF NONLINEAR EQUATIONS OF STURM-LIOUVILLE TYPE
cites work: Q4888374
cites work: Q5562938
cites work: Q4713493
cites work: Change of variables for absolutely continuous functions
DOI: 10.1016/J.JMAA.2004.12.051
description: scientific article; zbMATH DE number 2173099