We prove the existence of weak solutions for a 3D phase change model introduced by Michel Fre´mond 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 Fre´mond’s model provided all quantities in question are smooth enough.
|Titolo:||Existence of solutions to a phase transition model with microscopic movements|
ROCCA, ELISABETTA (Ultimo)
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2009|
|Digital Object Identifier (DOI):||10.1002/mma.1089|
|Appare nelle tipologie:||01 - Articolo su periodico|