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Analysis of a one-dimensional variational modelofthe equilibrium shapel of a deformable crystal

Published online by Cambridge University Press:  15 August 2002

Eric Bonnetier ,
Richard S. Falk  and
Michael A. Grinfeld
Eric Bonnetier
Affiliation:
CNRS-CMAP, École Polytechnique, 91128 Palaiseau, France. e-mail:
Richard S. Falk
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA. e-mail:
Michael A. Grinfeld
Affiliation:
Educational Testing Service, Princeton, NJ, USA. e-mail:
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Abstract

The equilibrium configurations of a one-dimensional variational model thatcombines terms expressing the bulk energy of a deformable crystal and itssurface energy are studied. After elimination of the displacement, theproblem reduces to the minimization of a nonconvex and nonlocal functional ofa single function, the thickness. Depending on a parameter which strengthensone of the terms comprising the energy at the expense of the other, it isshown that this functional may have a stable absolute minimum or only aminimizing sequence in which the term corresponding to the bulk energy isforced to zero by the production of a crack in the material.

Keywords

Equilibrium shapenon-convex energy functionalvariational problem.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 3 , May 1999 , pp. 573 - 591
Copyright
© EDP Sciences, SMAI, 1999

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