Existence of solutions to an anisotropic phase-field model

被引：13

作者：

Burman, E ^{[1
]}

Rappaz, J ^{[1
]}

机构：

[1] Ecole Polytech Fed Lausanne, IACS, CH-1015 Lausanne, Switzerland

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2003年 / 26卷 / 13期

关键词：

dendritic solidification; phase-field equations; monotone operators; strongly non-linear parabolic systems;

D O I：

10.1002/mma.405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an anisotropic phase-field model for the isothermal solidification of a binary alloy due to Warren-Boettinger (Acta. Metall. Mater. 1995; 43(2):689)., Existence of weak solutions is established under a certain convexity condition on the strongly non-linear second-order anisotropic operator and Lipschitz and boundedness assumptions for the non-linearities. A maximum principle holds that guarantees the existence of a solution under physical assumptions on the non-linearities. The qualitative properties of the solutions are illustrated by a numerical example. Copyright (C) 2003 John Wiley Sons, Ltd.

引用

页码：1137 / 1160

页数：24

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