Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals

Authors
Carpio, A Chapman, SJ Velazquez, JLL
Citation
A. Carpio et al., Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals, SIAM J A MA, 61(6), 2001, pp. 2168-2199
Citations number
18
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON APPLIED MATHEMATICS
ISSN journal
00361399 → ACNP
Volume
61
Issue
6
Year of publication
2001
Pages
2168 - 2199
Database
ISI
SICI code
0036-1399(20010522)61:6<2168:PSFSSO>2.0.ZU;2-L
Abstract
Some continuum models for dislocation interactions in a simple crystal geom etry are studied. The simplest models are mixed systems ofconservation laws which are shown to exhibit singularities and instabilities. These are then regularized, leading to parabolic free-boundary problems. In both cases, s olutions describing the formation of structures such as dislocation pile-up s are discussed.