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

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2001
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Society for Industrial and Applied Mathematics
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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.
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