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 variable.
Existence and boundedness of solutions for a singular phase field system
BONETTI, ELENA;COLLI, PIERLUIGI;GILARDI, GIANNI MARIA
2009-01-01
Abstract
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 variable.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
