Existence and boundedness of solutions for a singular phase field system

This paper is devoted to the mathematical analysis of a thermomechanical
model describing phase transitions in terms of the
entropy and order structure balance law. We consider a macroscopic
description of the phenomenon and make a presentation
of the model. Then, the initial and boundary value problem is addressed
for the related PDE system, which contains some nonlinear
and singular terms with respect to the temperature variable. Existence
of the solution is shown along with the boundedness of both
phase variable and absolute temperature . Finally, uniqueness
is proved in the framework of a source term depending Lipschitz
continuously on the temperature.