ON THE NONCONSERVED CAGINALP PHASE-FIELD SYSTEM BASED ON THE MAXWELL-CATTANEO LAW WITH TWO TEMPERATURES AND LOGARITHMIC POTENTIALS

摘要

Our aim in this article is to study generalizations of the nonconserved 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 system. In particular, we prove the existence of the global attractor. Furthermore, we give some numerical simulations, obtained with the FreeFem++ software [24], comparing the nonconserved Caginalp phase-field model with regular and logarithmic nonlinear terms.