arXiv:1007.2915 Abstract | arXiv Analytics

arXiv:1007.2915 [math.AP]Abstract References Reviews Resources

Homogenization of the Peierls-Nabarro model for dislocation dynamics

Published 2010-07-17, updated 2012-07-18Version 2

This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic L\'{e}vy operator of order 1 and a potential depending periodically on $u/\ep$. The limit equation is a non-local Hamilton-Jacobi equation, which is an effective plastic law for densities of dislocations moving in a single slip plane.

Comments: 39 pages

Categories: math.AP

Keywords: peierls-nabarro model, homogenization, integro-differential equation describing dislocation dynamics, non-local hamilton-jacobi equation, single slip plane

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