Global existence of a strong solution to the one-dimensional full model for irreversible phase transitions

This note deals with the analysis of a model proposed by M. Fremond in order to describe some irreversible phase transition phenomena resulting as macroscopic effects of the microscopic movements of molecules. This model consists in a nonlinear system of partial differential equations of parabolic type and several simplifications have been studied recently. Nevertheless, up to now the question of the existence of a solution to the full problem was still open. This paper answers affirmatively to this question in the one dimensional setting by exploiting a regularization -- a priori estimates -- passage to the limit procedure