We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified assumptions on the strain energy and data we prove the existence and uniqueness of a regular solution to the problem. The proof is based on the Leray-Schauder fixed point theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-2,
author = {Zenon Kosowski},
title = {Unique global solvability of 1D Fried-Gurtin model},
journal = {Applicationes Mathematicae},
volume = {34},
year = {2007},
pages = {269-288},
zbl = {1133.35302},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-2}
}
Zenon Kosowski. Unique global solvability of 1D Fried-Gurtin model. Applicationes Mathematicae, Tome 34 (2007) pp. 269-288. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-2/