A reformulation of the Caginalp phase-field system based on the Maxwell-Cattaneo law

Our aim in this paper is to study the well-posedness and the dissipativity for a reformulation of the Caginalp phase-field system based on the Maxwell-Cattaneo law, instead of the usual Fourier law, for heat conduction. In particular, instead of the equation for the relative temperature (or the thermal displacement variable), we consider here the equation for the enthalpy.