This paper is devoted to the mathematical analysis of a thermomechanical model describing phase transitions in terms of the entropy and order structure balance law. We consider a macroscopic description of the phenomenon and make a presentation of the model. Then, the initial and boundary value problem is addressed for the related PDE system, which contains some nonlinear and singular terms with respect to the temperature variable. Existence of the solution is shown along with the boundedness of both phase variable and absolute temperature . Finally, uniqueness is proved in the framework of a source term depending Lipschitz continuously on the temperature.
Existence and boundedness of solutions for a singular phase field system
Bonetti E;Colli P;Gilardi G
2009
Abstract
This paper is devoted to the mathematical analysis of a thermomechanical model describing phase transitions in terms of the entropy and order structure balance law. We consider a macroscopic description of the phenomenon and make a presentation of the model. Then, the initial and boundary value problem is addressed for the related PDE system, which contains some nonlinear and singular terms with respect to the temperature variable. Existence of the solution is shown along with the boundedness of both phase variable and absolute temperature . Finally, uniqueness is proved in the framework of a source term depending Lipschitz continuously on the temperature.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.