Existence and boundedness of solutions for a singular phase field system

2008/04/10 by E. Bonetti, Bonetti, Elena, Pierluigi Colli +5
Materials Science · Computer Science · Engineering · #Solidification and crystal growth phenomena #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0804.1628

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 χ and absolute temperature θ. Finally, uniqueness is proved in the framework of a source term depending Lipschitz continuously on θ.

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