Phase separation in a gravity field

Pavel Krejčí; Elisabetta Rocca; Jürgen Sprekels

doi:10.3934/dcdss.2011.4.391

Article Contents

2011, Volume 4, Issue 2: 391-407. Doi: 10.3934/dcdss.2011.4.391

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Phase separation in a gravity field

1.
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1
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: April 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 80A22; Secondary: 74C05, 35K50.

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