Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy
type: Item
instance of: scholarly article
title: Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy
zbMATH Open document ID: 1160.49010
DOI: 10.4171/IFB/204
author: Andrea Braides
author: Caterina Ida Zeppieri
published in: Interfaces and Free Boundaries
publication date: 2009-05-13T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: Summary: The combined effect of fine heterogeneities and small gradient perturbations is analyzed by means of an asymptotic development by \(\varGamma\)-convergence for a family of energies related to (one-dimensional) phase transformations. We show that multi-scale effects add up to the usual sharp-interface limit, due to the homogenization of microscopic interfaces, internal and external boundary layers, optimal arrangements of microscopic oscillations, etc. Several regimes are analyzed depending on the ``size'' of the heterogeneity (small or large perturbations of a homogeneous situation) and their relative period as compared with the characteristic length of the phase transitions (slow or fast oscillations).
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 82B26
Mathematics Subject Classification ID: 74Q99
zbMATH DE Number: 5553696
zbMATH Keywords: \(\varGamma \)-convergence
zbMATH Keywords: \(\varGamma \)-development
zbMATH Keywords: phase transitions
zbMATH Keywords: homogenization
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5553696