Global smooth solution to the standard phase-field model with memory

Abstract

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.