A phase-field system with two temperatures and memory

We consider a generalization of the Caginalp phase-field system based on the Gurtin--Pipkin law with two temperatures for heat conduction with memory. In particular, we obtain well-posedness results and study the dissipativity, in terms of the global attractor with optimal regularity, of the associated solution operators. We also study the stability of the system as the memory kernel collapses to a Dirac mas