Abstract
In this article, we present briefly the 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.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Cardaliaguet, P., Da Lio, F., Forcadel, N., Monneau, R. (2006). Dislocation Dynamics: a Non-local Moving Boundary. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_13
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DOI: https://doi.org/10.1007/978-3-7643-7719-9_13
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