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Numerical solution of nonlinear hypersingular integral equations of the Peierls type in dislocation theory
Univ Cent Lancashire, Ctr Res Fire & Explos Studies, Preston PR1 2HE, Lancs, England Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 9EW, England.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Univ Cent Lancashire, Ctr Res Fire & Explos Studies, Preston PR1 2HE, Lancs, England Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 9EW, England.
Univ Cent Lancashire, Ctr Res Fire & Explos Studies, Preston PR1 2HE, Lancs, England Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 9EW, England.
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2000 (English)In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 60, no 2, 664-678 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we analyze hypersingular integral equations of the Peierls type specified on the whole real axis. The method of "approximate approximations" [Maz'ya, Proceedings of the Eighth Conference on the Mathematics of Finite 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 dislocations. The critical Peierls stress is evaluated for different configurations of dislocations and for different types of the interatomic force law.

Place, publisher, year, edition, pages
2000. Vol. 60, no 2, 664-678 p.
Keyword [en]
hypersingular integral equations, dislocations
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-49834OAI: oai:DiVA.org:liu-49834DiVA: diva2:270730
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-12

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Maz´ya, Vladimir G.

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