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Analysis of a one-dimensional variational model ofthe equilibrium shapel of a deformable crystal
Published online by Cambridge University Press: 15 August 2002
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.
- 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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