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

Carpio Rodríguez, Ana María 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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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
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Deposited On:04 May 2012 11:44
Last Modified:06 Feb 2014 10:16

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