American Institute of Mathematical Sciences

April  2011, 4(2): 391-407. doi: 10.3934/dcdss.2011.4.391

Phase separation in a gravity field

 1 Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1, Czech Republic 2 WIAS Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany, Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano 3 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D–10117 Berlin

Received  May 2009 Revised  August 2009 Published  November 2010

We prove here well-posedness and convergence to equilibria for the solution trajectories associated with a model for solidification of the liquid content of a rigid container in a gravity field. We observe that the gravity effects, which can be neglected without considerable changes of the process on finite time intervals, have a substantial influence on the long time behavior of the evolution system. Without gravity, we find a temperature interval, in which all phase distributions with a prescribed total liquid content are admissible equilibria, while, under the influence of gravity, the only equilibrium distribution in a connected container consists in two pure phases separated by one plane interface perpendicular to the gravity force.
Citation: Pavel Krejčí, Elisabetta Rocca, Jürgen Sprekels. Phase separation in a gravity field. Discrete & Continuous Dynamical Systems - S, 2011, 4 (2) : 391-407. doi: 10.3934/dcdss.2011.4.391
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