This paper is devoted to study the so-called phase-field model when the classical Fourier law is replaced by the Gurtin-Pipkin constitutive assumption. The resulting system of partial differential equations is investigated in a quite general setting. A hyperbolic equation is coupled with a parabolic variational inequality, the state variables being temperature and non-conserved order parameter. By including initial and boundary conditions, the existence and uniqueness of strong solutions is shown along with regularity results ensuring the global boundedness of both the unknowns.
"Global smooth solution to the standard phase-field model with memory." Adv. Differential Equations 2 (3) 453 - 486, 1997.