On the Conserved Caginalp Phase-Field System with Logarithmic Potentials Based on the Maxwell–Cattaneo Law with Two Temperatures

Abstract

Our aim in this article is to study generalizations of the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures for heat conduction and with logarithmic nonlinear terms. We obtain well-posedness results and study the asymptotic behavior of the associated system. In particular, we prove the existence of the global attractor and prove the strict separation to the pure phases in two space dimensions. Furthermore, we give some numerical simulations, obtained with the FreeFem++ software [23], comparing the conserved Caginalp phase-field type model with regular and with logarithmic nonlinear terms.