Unique global solvability of 1D Fried-Gurtin model

Zenon Kosowski. "Unique global solvability of 1D Fried-Gurtin model." Applicationes Mathematicae 34.3 (2007): 269-288. <http://eudml.org/doc/280011>.

@article{ZenonKosowski2007,
abstract = {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.},
author = {Zenon Kosowski},
journal = {Applicationes Mathematicae},
keywords = {solid-solid transition; phase-field theory; Leray-Schauder theory},
language = {eng},
number = {3},
pages = {269-288},
title = {Unique global solvability of 1D Fried-Gurtin model},
url = {http://eudml.org/doc/280011},
volume = {34},
year = {2007},
}

TY - JOUR
AU - Zenon Kosowski
TI - Unique global solvability of 1D Fried-Gurtin model
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 3
SP - 269
EP - 288
AB - 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.
LA - eng
KW - solid-solid transition; phase-field theory; Leray-Schauder theory
UR - http://eudml.org/doc/280011
ER -