In this article, we present briefly a mathematical study of the dynamics of line defects called dislocations, in crystals. The mathematical model is an eikonal equation describing the motion of the dislocation line with a velocity which is a non-local function of the whole shape of the dislocation. We present some partial existence and uniqueness results. Finally, we also show that the self-dynamics of a dislocation line at large scale is asymptotically described by an anisotropic mean curvature motion.'

Dislocation Dynamics: a Non-local Moving Boundary

DA LIO, FRANCESCA;
2007

Abstract

In this article, we present briefly a mathematical study of the dynamics of line defects called dislocations, in crystals. The mathematical model is an eikonal equation describing the motion of the dislocation line with a velocity which is a non-local function of the whole shape of the dislocation. We present some partial existence and uniqueness results. Finally, we also show that the self-dynamics of a dislocation line at large scale is asymptotically described by an anisotropic mean curvature motion.'
2007
Free boundary problems.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2527122
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