Analysis of a three-dimensional phase-field model for solidification under a magnetic field effect

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Ferreira e Pereira, Andre¹  Planas, Gabriela¹ 

[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP, Brazil

关键词: Phase-field model;    Solidificatioh;    Convection;    Magnetic effect;    Degenerate parabolic systems;   

DOI  :  10.1016/j.jmaa.2019.123494

来源: Elsevier

【 摘 要 】

This paper presents a mathematical analysis to a three-dimensional isothermal model of solidification for a binary alloy with melt convection and under a magnetic field effect. The model consists of a highly non-linear system of partial differential equations for the state variables: the velocity field, the pressure, the potential function of the electrical field, the phase-field which represents the solid/liquid phase of the alloy, and the concentration. The well-posedness of the model is discussed. Moreover, the existence of solutions when the diffusion coefficient of the concentration equation vanishes for some values of the phase-field is investigated. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free