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

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Carpio, Ana and Chapman, S.J. and Velázquez, J.J. 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 0036-1399

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Official URL: http://epubs.siam.org/siap/resource/1/smjmap/v61/i6/p2168_s1?isAuthorized=no


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Abstract

Some continuum models for dislocation interactions in a simple crystal geometry 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, 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:Sciences > Physics > Mathematical physics
Sciences > Mathematics > Differential equations
ID Code:15097
Deposited On:04 May 2012 11:44
Last Modified:12 Dec 2018 15:07

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