Existence of solutions to a phase transition model with microscopic movements

We prove the existence of weak solutions for a 3D phase change model introduced by Michel Fremond 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 Fremond's model provided all quantities in question are smooth enough. Copyright (C) 2008 John Wiley & Sons, Ltd.