The Mathematical Institute, University of Oxford, Eprints Archive

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

Carpio, Ana and Chapman, S. J. and Velazquez, J. L. L. (2001) Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals. SIAM Journal on Applied Mathematics, 61 (6). pp. 2168-2199. ISSN 1095-712X

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Official URL: http://www.siam.org/journals/siap/61-6/36434.html

Abstract

Some continuum models for dislocation interactions in a simple crystal geometry are studied. The simplest models are mixed systems of conservation laws which are shown to exhibit singularities and instabilities. These are then regularized, leading to parabolic free-boundary problems. In both cases, solutions describing the formation of structures such as dislocation pile-ups are discussed.

Item Type:Article
Uncontrolled Keywords:dislocation dynamics; degenerate systems of conservation laws; free-boundary problems; pattern formation
Subjects:H - N > Mechanics of deformable solids
O - Z > Partial differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:606
Deposited By:Jon Chapman
Deposited On:24 May 2007
Last Modified:20 Jul 2009 14:22

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