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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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 |
|---|---|
| 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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