The paper deals with the asymptotic behaviour of a family of integral functionals in the framework of phase separation. In order to obtain a selection criterion for the minima of the usual double-well, non-convex free energy involving the phase-variable u, we add a gradient term in a new variable v which is related to u through the L2-distance between u and v, weighted by a coefficient α. We prove that the limit is a minimal area model with a surface tension of non-local form. The well-known Modica-Mortola constant can be recovered in this setting as a limit case when α tends to infinity.
Variational models for phase separation
VITALI, ENRICO;SOLCI, MARGHERITA
2003-01-01
Abstract
The paper deals with the asymptotic behaviour of a family of integral functionals in the framework of phase separation. In order to obtain a selection criterion for the minima of the usual double-well, non-convex free energy involving the phase-variable u, we add a gradient term in a new variable v which is related to u through the L2-distance between u and v, weighted by a coefficient α. We prove that the limit is a minimal area model with a surface tension of non-local form. The well-known Modica-Mortola constant can be recovered in this setting as a limit case when α tends to infinity.File in questo prodotto:
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