Publication 18-CNA-026

A Note On Homogenization Effects On Phase Transition Problems

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

Abstract: In fluid-fluid phase transitions problems featuring small scale heterogeneity, we see that when the scale heterogeneity is sufficiently small, the periodic potential function $W(x,p)$ can be replaced with a homogenized potential function $W_H(p)$. This allows for a reduction to a problem already studied by Fonseca and Tartar [6]. In particular, we see an isotropic transition potential, in contrast with the case where the scales are roughly comensurate [4]. This note is intended as a prelude to a more complete analysis of the full range of scales.

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