## N. Dirr - M. Lucia - M. Novaga

# Gradient theory of phase transitions with a rapidly oscillating forcing term

created by novaga on 03 Oct 2007

modified on 10 Nov 2018

[

BibTeX]

*Published Paper*

**Inserted:** 3 oct 2007

**Last Updated:** 10 nov 2018

**Journal:** Asymptotic Analysis

**Volume:** 60

**Pages:** 29-59

**Year:** 2008

**Abstract:**

We consider the Gamma-limit of a family of functionals which
model the interaction of a material that undergoes phase
transition with a rapidly oscillating conservative vector field.
These functionals consist of a gradient term, a double-well
potential and a vector field. The scaling is such that all three
terms scale in the same way and the frequency of the vector field
is equal to the interface thickness. Difficulties arise from the
fact that the two global minimizers of the functionals are
nonconstant and converge only in the weak $L^2$-topology.

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