Homogenization of periodic systems with large potentials
type: Item
instance of: scholarly article
title: Homogenization of periodic systems with large potentials
zbMATH Open document ID: 1072.35023
author: Grégoire Allaire
author: Yves Capdeboscq
author: Vincent Siess
author: A. Piatnitski
author: Muthusamy Vanninathan
published in: Archive for Rational Mechanics and Analysis
publication date: 2005-03-02T00:00:00Z
review text: Consider a system of second order equation in a periodic medium with a large potential (if \(\epsilon\) denotes the period the potential is scaled as \(\epsilon^{-2}\). Under some spectral assumptions on the cell problem the authors prove that the solution can be factorized as a product of a fast oscillating cell eigenfunction and of a slowly varying solution of a scalar second order equation. The result applies to the parabolic case as well as to the hyperbolic one and also to a fourth order plate equation. The methods used are a combination of the two scales convergence method, oscillating test functions methods and Bloch wave decomposition method.
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 74Q05
Mathematics Subject Classification ID: 74Q10
zbMATH DE Number: 2140284
zbMATH Keywords: two scales convergence method
zbMATH Keywords: oscillating test functions methods
zbMATH Keywords: Bloch wave decomposition method
MaRDI profile type: Publication
full work available at URL: s00205-004-0332-7
OpenAlex ID: W2129410468
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DOI: 10.1007/S00205-004-0332-7
description: scientific article; zbMATH DE number 2140284