Singular perturbation models in phase transitions for second-order materials
type: Item
instance of: scholarly article
title: Singular perturbation models in phase transitions for second-order materials
zbMATH Open document ID: 1255.49022
author: M. Chermisi
author: G. Leoni
author: G. Dal Maso
author: Irene Fonseca
published in: Indiana University Mathematics Journal
publication date: 2012-07-11T00:00:00Z
full work available at URL: http://www.iumj.indiana.edu/IUMJ/ABS/2011/4346
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35Q56
Mathematics Subject Classification ID: 49S05
zbMATH DE Number: 6054376
zbMATH Keywords: \(\Gamma\)-convergence
zbMATH Keywords: singular perturbation
zbMATH Keywords: higher-order derivatives
zbMATH Keywords: pattern formation
zbMATH Keywords: interpolation inequalities
Wikidata QID: Q61442424
MaRDI profile type: Publication
OpenAlex ID: W2068826680
DOI: 10.1512/IUMJ.2011.60.4346
review text: The authors use the \(\Gamma\)-convergence technique to characterize the singular perturbation limit of a family of rescaled energies \(F(u,\Omega)\) for dimensions \(n>1\) (the analysis for \(n=1\) was obtained by other authors). Here \(u\) represents the energy and \(\Omega\) is a bounded domain. The limiting functional \(F\) provides the effective energy on the phase transition surface.NEWLINENEWLINE The onset of pattern formation in the two component bilinear membranes and amphiphilic monolayers leads to the analysis of the energy \(u\) which includes the stiffness coefficient (\(-q\)). Authors found that curvature instabilities and pattern formation will occur when (\(-q\)) is negative. Compactness results are obtained in addition to an integral representation of the limit energy.
reviewed by: Shlomo Carmi
description: scientific article; zbMATH DE number 6054376