Phase change problems with temperature dependent constraints for the volume fraction velocities

A class of nonlinear systems of parabolic PDEs is considered as a mathematical model for phase change phenomena arising in binary mixtures. We use the volume fraction of one of the components as an order parameter in our systems. Therefore, our system consists of two kinetic equations for the internal energy and order parameter which are derived in the non-smooth thermomechanics theory. In this paper we give a general treatment for our system and establish an existence result by applying the Schauder's fixed point theory with the subdifferential operator techniques.