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Existence of solutions to a phase transition model with microscopic movements

✍ Scribed by Eduard Feireisl; Hana Petzeltová; Elisabetta Rocca

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
212 KB
Volume
32
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We prove the existence of weak solutions for a 3D phase change model introduced by Michel Frémond in (Non‐smooth Thermomechanics. Springer: Berlin, 2002) showing, via a priori estimates, the weak sequential stability property in the sense already used by the first author in (Comput. Math. Appl. 2007; 53:461–490). The result follows by passing to the limit in an approximate problem obtained adding a superlinear part (in terms of the gradient of the temperature) in the heat flux law. We first prove well posedness for this last problem and then—using proper a priori estimates—we pass to the limit showing that the total energy is conserved during the evolution process and proving the non‐negativity of the entropy production rate in a suitable sense. Finally, these weak solutions turn out to be the classical solution to the original Frémond's model provided all quantities in question are smooth enough. Copyright © 2008 John Wiley & Sons, Ltd.

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