# Minimizing movements for dislocation dynamics with a mean curvature term

Nicolas Forcadel; Aurélien Monteillet

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- Volume: 15, Issue: 1, page 214-244
- ISSN: 1292-8119

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topForcadel, Nicolas, and Monteillet, Aurélien. "Minimizing movements for dislocation dynamics with a mean curvature term." ESAIM: Control, Optimisation and Calculus of Variations 15.1 (2009): 214-244. <http://eudml.org/doc/250605>.

@article{Forcadel2009,

abstract = {
We prove existence of minimizing movements for the
dislocation dynamics evolution law of a propagating front, in which the normal velocity of the front is the sum of a non-local term and a mean curvature term. We prove that any such minimizing movement is a weak solution of this evolution law, in a sense related to viscosity
solutions of the corresponding level-set equation. We also prove the
consistency of this approach, by showing that any minimizing movement
coincides with the smooth evolution as long as the latter exists. In
relation with this, we finally prove short time existence and uniqueness of a smooth
front evolving according to our law, provided the initial shape is
smooth enough.
},

author = {Forcadel, Nicolas, Monteillet, Aurélien},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Front propagation; non-local equations; dislocation dynamics; mean curvature motion; viscosity solutions; minimizing movements; sets of finite perimeter; currents; front propagation},

language = {eng},

month = {1},

number = {1},

pages = {214-244},

publisher = {EDP Sciences},

title = {Minimizing movements for dislocation dynamics with a mean curvature term},

url = {http://eudml.org/doc/250605},

volume = {15},

year = {2009},

}

TY - JOUR

AU - Forcadel, Nicolas

AU - Monteillet, Aurélien

TI - Minimizing movements for dislocation dynamics with a mean curvature term

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2009/1//

PB - EDP Sciences

VL - 15

IS - 1

SP - 214

EP - 244

AB -
We prove existence of minimizing movements for the
dislocation dynamics evolution law of a propagating front, in which the normal velocity of the front is the sum of a non-local term and a mean curvature term. We prove that any such minimizing movement is a weak solution of this evolution law, in a sense related to viscosity
solutions of the corresponding level-set equation. We also prove the
consistency of this approach, by showing that any minimizing movement
coincides with the smooth evolution as long as the latter exists. In
relation with this, we finally prove short time existence and uniqueness of a smooth
front evolving according to our law, provided the initial shape is
smooth enough.

LA - eng

KW - Front propagation; non-local equations; dislocation dynamics; mean curvature motion; viscosity solutions; minimizing movements; sets of finite perimeter; currents; front propagation

UR - http://eudml.org/doc/250605

ER -

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