# Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics

Francesca Da Lio; N. Forcadel; Régis Monneau

Journal of the European Mathematical Society (2008)

- Volume: 010, Issue: 4, page 1061-1104
- ISSN: 1435-9855

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topDa Lio, Francesca, Forcadel, N., and Monneau, Régis. "Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics." Journal of the European Mathematical Society 010.4 (2008): 1061-1104. <http://eudml.org/doc/277256>.

@article{DaLio2008,

abstract = {We prove the convergence at a large scale of a non-local first order equation to an
anisotropic mean curvature motion. The equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, which arises in the theory of dislocation dynamics. We show that if an anisotropic mean curvature motion is approximated by equations of this type then it is always of variational type, whereas the converse is true only in dimension two.},

author = {Da Lio, Francesca, Forcadel, N., Monneau, Régis},

journal = {Journal of the European Mathematical Society},

keywords = {dislocations dynamics; asymptotic behavior; non-local equations; eikonal equation; mean curvature motion; viscosity solutions; non-local equations; viscosity solutions},

language = {eng},

number = {4},

pages = {1061-1104},

publisher = {European Mathematical Society Publishing House},

title = {Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics},

url = {http://eudml.org/doc/277256},

volume = {010},

year = {2008},

}

TY - JOUR

AU - Da Lio, Francesca

AU - Forcadel, N.

AU - Monneau, Régis

TI - Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics

JO - Journal of the European Mathematical Society

PY - 2008

PB - European Mathematical Society Publishing House

VL - 010

IS - 4

SP - 1061

EP - 1104

AB - We prove the convergence at a large scale of a non-local first order equation to an
anisotropic mean curvature motion. The equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, which arises in the theory of dislocation dynamics. We show that if an anisotropic mean curvature motion is approximated by equations of this type then it is always of variational type, whereas the converse is true only in dimension two.

LA - eng

KW - dislocations dynamics; asymptotic behavior; non-local equations; eikonal equation; mean curvature motion; viscosity solutions; non-local equations; viscosity solutions

UR - http://eudml.org/doc/277256

ER -

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