Publication 18-CNA-016

A Homogenization Result In The Gradient Theory Of Phase Transitions

Riccardo Cristoferi
Department of Mathematical Sciences
Heriot-Watt University
Edinburgh EH14 4AS, United Kingdom
r.cristoferi@hw.ac.uk

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Adrian Hagerty
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
ahagerty@andrew.cmu.edu

Cristina Popovici
Department of Mathematics and Statistics
Loyola University Chicago
cpopovici@luc.edu

Abstract: A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In particular, the case where the scale ε of the small homogeneities is of the same order of the scale governing the phase transition is considered. The interaction between homogenization and the phase transitions process will lead, in the limit as ε → 0, to an anisotropic interfacial energy.

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