Existence of strong solutions for a fully hyperbolic phase-field model based on type III heat conduction with a logarithmic nonlinear term (Q2254938)

The author is concerned with the existence and uniqueness of global strong solutions to a phase-field model that involves a nonlinear term of logarithmic type in the equation for the order parameter. Both the parabolic and fully hyperbolic variants of the model are analyzed. The proofs are based on delicate a priori estimates. The paper generalizes earlier results by \textit{M. Grasselli} et al. [Math. Nachr. 280, No. 13--14, 1475--1509 (2007; Zbl 1133.35017)], and the author and \textit{R. Quintanilla} [Appl. Math. Lett. 24, No. 6, 1003--1008 (2011; Zbl 1213.35187)].