Carpio, Ana and Chapman, S. J. and Velazquez, J. L. 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 1095-712X

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Official URL: http://www.siam.org/journals/siap/61-6/36434.html

## Abstract

Some continuum models for dislocation interactions in a simple crystal geometry are studied. The simplest models are mixed systems of conservation 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 |
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Uncontrolled Keywords: | dislocation dynamics; degenerate systems of conservation laws; free-boundary problems; pattern formation |

Subjects: | H - N > Mechanics of deformable solids O - Z > Partial differential equations |

Research Groups: | Oxford Centre for Industrial and Applied Mathematics |

ID Code: | 606 |

Deposited By: | Jon Chapman |

Deposited On: | 24 May 2007 |

Last Modified: | 20 Jul 2009 14:22 |

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