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
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.
|Uncontrolled Keywords:||Dislocation dynamics, degenerate systems of conservation laws, free-boundary problems, pattern formation|
|Subjects:||Sciences > Physics > Mathematical physics|
Sciences > Mathematics > Differential equations
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|Deposited On:||04 May 2012 11:44|
|Last Modified:||20 Apr 2015 12:15|
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