Citation
V. Karlin et al., Numerical solution of nonlinear hypersingular integral equations of the Peierls type in dislocation theory, SIAM J A MA, 60(2), 2000, pp. 664-678
Citations number
15
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON APPLIED MATHEMATICS
ISSN journal
00361399
→ ACNP
Volume
60
Issue
2
Year of publication
2000
Pages
664 - 678
Database
ISI
SICI code
0036-1399(20000202)60:2<664:NSONHI>2.0.ZU;2-2
Abstract
In this paper we analyze hypersingular integral equations of the Peierls ty
pe specified on the whole real axis. The method of "approximate approximati
ons" [Maz'ya, Proceedings of the Eighth Conference on the Mathematics of Fi
nite Elements and Applications, VIII, MAFELAP 1993, Brunel University, 1994
, pp. 107-104] is employed in order to produce numerical solutions of high
accuracy, and the results are applied to problems in the theory of dislocat
ions. The critical Peierls stress is evaluated for different configurations
of dislocations and for different types of the interatomic force law.