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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