Existence of solutions to a phase transition model with microscopic movements |
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Authors: | Eduard Feireisl Hana Petzeltová Elisabetta Rocca |
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Institution: | 1. Czech Academy of Sciences, Institute of Mathematics, ?itná 25, CZ‐11567 Praha 1, Czech Republic;2. Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy |
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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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Keywords: | nonlinear PDE system global existence uniqueness phase transitions |
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