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 prob- lems. In both cases, solutions describing the formation of structures such as dislocation pile-ups are discussed.
['Ana Carpio', 'S. J. Chapman', 'Justiniano Velázquez']
PILE-UP SOLUTIONS FOR SOME SYSTEMS OF CONSERVATION LAWS MODELLING DISLOCATION INTERACTION IN CRYSTALS ∗