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

Da 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 -