Existence of Strong Solutions for a Fully Hyperbolic Phase-Field Model Based on Type III Heat Conduction with a Logarithmic Nonlinear Term

In this paper, we prove the existence (and also the uniqueness) of strong solutions for a fully hyperbolic phase-field model based on type III heat conduction. The model consists of the hyperbolic relaxation of the usual equation for the temperature, coupled with the equation for the thermal displacement variable. We also study the limit problem, as the relaxation parameter goes to 0.