top
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.
Zenon Kosowski. "Global existence of weak solutions to the Fried-Gurtin model of phase transitions." Applicationes Mathematicae 34.4 (2007): 413-430. <http://eudml.org/doc/279925>.
@article{ZenonKosowski2007, abstract = {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.}, author = {Zenon Kosowski}, journal = {Applicationes Mathematicae}, keywords = {Fried-Gurtin model; solid-solid transition; phase-field theory; existence and uniqueness of weak solution; Faedo-Galerkin method; hyperbolic-parabolic system; three-dimensional system; order parameter; energy estimates}, language = {eng}, number = {4}, pages = {413-430}, title = {Global existence of weak solutions to the Fried-Gurtin model of phase transitions}, url = {http://eudml.org/doc/279925}, volume = {34}, year = {2007}, }
TY - JOUR AU - Zenon Kosowski TI - Global existence of weak solutions to the Fried-Gurtin model of phase transitions JO - Applicationes Mathematicae PY - 2007 VL - 34 IS - 4 SP - 413 EP - 430 AB - 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. LA - eng KW - Fried-Gurtin model; solid-solid transition; phase-field theory; existence and uniqueness of weak solution; Faedo-Galerkin method; hyperbolic-parabolic system; three-dimensional system; order parameter; energy estimates UR - http://eudml.org/doc/279925 ER -