Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal

Bonnetier, Eric, Falk, Richard S., and Grinfeld, Michael A.. "Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal." ESAIM: Mathematical Modelling and Numerical Analysis 33.3 (2010): 573-591. <http://eudml.org/doc/197404>.

@article{Bonnetier2010,
abstract = { The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a stable absolute minimum or only a minimizing sequence in which the term corresponding to the bulk energy is forced to zero by the production of a crack in the material. },
author = {Bonnetier, Eric, Falk, Richard S., Grinfeld, Michael A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Equilibrium shape; non-convex energy functional; variational problem.; minimization of nonconvex nonlocal functional; equilibrium configurations; one-dimensinal variational model; bulk energy; deformable crystal; surface energy; stable absolute minimum; minimizing sequence},
language = {eng},
month = {3},
number = {3},
pages = {573-591},
publisher = {EDP Sciences},
title = {Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal},
url = {http://eudml.org/doc/197404},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Bonnetier, Eric
AU - Falk, Richard S.
AU - Grinfeld, Michael A.
TI - Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 3
SP - 573
EP - 591
AB - The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a stable absolute minimum or only a minimizing sequence in which the term corresponding to the bulk energy is forced to zero by the production of a crack in the material.
LA - eng
KW - Equilibrium shape; non-convex energy functional; variational problem.; minimization of nonconvex nonlocal functional; equilibrium configurations; one-dimensinal variational model; bulk energy; deformable crystal; surface energy; stable absolute minimum; minimizing sequence
UR - http://eudml.org/doc/197404
ER -