We prove the existence of global in time weak solutions to a three-dimensional system of equations arising in a simple version of the Fried-Gurtin model for the isothermal phase transition in solids. In this model the phase is characterized by an order parameter. The problem considered here has the form of a coupled system of three-dimensional elasticity and parabolic equations. The system is studied with the help of the Faedo-Galerkin method using energy estimates.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-5,
author = {Zenon Kosowski},
title = {Global existence of weak solutions to the Fried-Gurtin model of phase transitions},
journal = {Applicationes Mathematicae},
volume = {34},
year = {2007},
pages = {413-430},
zbl = {1134.35024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-5}
}
Zenon Kosowski. Global existence of weak solutions to the Fried-Gurtin model of phase transitions. Applicationes Mathematicae, Tome 34 (2007) pp. 413-430. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-4-5/