A free-boundary problem modeling loop dislocations in crystals
type: Item
instance of: scholarly article
title: A free-boundary problem modeling loop dislocations in crystals
zbMATH Open document ID: 0776.73009
DOI: 10.1007/BF00381671
author: A. Friedman
author: Bei Hu
author: Juan J. Velázquez
published in: Archive for Rational Mechanics and Analysis
publication date: 1993-02-18T00:00:00Z
review text: The authors are dealing with the mathematical Berucki model studied numerically a loop dislocation whose shape is a torus generated by a rotation of a disc of unit radius about an axis. The rate of change of \(R(t)\), being the distance from the axis, is roughly given by the fluxes of intersticials and vacancies. The problem of the formation of dislocations is solved as a free-boundary problem for the torus. Some simplified problems are treated in one-, two- and three-dimensional cases. The existence and uniqueness theorems for their solutions are presented and proved. It is shown that there is a class of initial data for which the solution does not exist. A travelling wave solution is constructed and the complete three-dimensional problem with data close to it is concerned.
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74M25
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 124150
zbMATH Keywords: torus model
zbMATH Keywords: Berucki model
zbMATH Keywords: formation of dislocations
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: travelling wave solution
Wikidata QID: Q116009595
reviewed by: Sitiro Minagawa
MaRDI profile type: Publication
cites work: Q5520962
cites work: Analyticity of the free boundary for the Stefan problem
cites work: Q2965997
full work available at URL: https://doi.org/10.1007/bf00381671
OpenAlex ID: W2018645841
description: scientific article; zbMATH DE number 124150