Geodesic
Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics
Journal of the European Mathematical Society, Tome 10 (2008) no. 4, pp. 1061-1104 Cet article a éte moissonné depuis la source EMS Press

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In this paper we prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. This first order equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, that arises in the theory of dislocations dynamics. We show that if an anisotropic mean curvature motion is approximated by this type of equations then it is always of variational type, whereas the converse is true only in dimension two.
DOI : 10.4171/jems/140
Classification : 35-XX, 00-XX
Keywords: Dislocations dynamics, asymptotic behavior, non-local equations, eikonal equation, mean curvature motion, viscosity solutions 
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     author = {Francesca Da Lio and Nicolas Forcadel and R\'egis Monneau},
     title = {Convergence of a non-local eikonal equation to anisotropic mean curvature motion. {Application} to dislocations dynamics},
     journal = {Journal of the European Mathematical Society},
     pages = {1061--1104},
     year = {2008},
     volume = {10},
     number = {4},
     doi = {10.4171/jems/140},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/140/}
}
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Francesca Da Lio; Nicolas Forcadel; Régis Monneau. Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics. Journal of the European Mathematical Society, Tome 10 (2008) no. 4, pp. 1061-1104. doi: 10.4171/jems/140

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