Interfaces and Free Boundaries


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Volume 7, Issue 2, 2005, pp. 187–197
DOI: 10.4171/IFB/120

Published online: 2005-06-30

An upper bound on the coarsening rate for mushy zones in a phase-field model

Shibin Dai[1] and Robert L. Pego[2]

(1) University of Maryland, College Park, USA
(2) Carnegie Mellon University, Pittsburgh, USA

We prove an upper bound on the coarsening rate for solutions of a phase field model with arbitrarily complicated patterns of phases. The analysis is performed in a regime corresponding to the late stages of phase separation, in which the ratio between the transition layer thickness and the length scale of the pattern is small, and is also small compared to the square of the ratio between the pattern scale and the system size. The analysis extends the method of Kohn and Otto (Comm.\ Math.\ Phys.\ 229 (2002), 375-395) to deal with both temperature and phase fields.

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Dai Shibin, Pego Robert: An upper bound on the coarsening rate for mushy zones in a phase-field model. Interfaces Free Bound. 7 (2005), 187-197. doi: 10.4171/IFB/120