Numerical simulation and linear well-posedness analysis for a class of three-phase boundary motion problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Pan, Zhenguo¹  Wetton, Brian² 

[1] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

关键词: Grain boundary;    Curvature motion;    Surface diffusion;    Three-phase problem;    Well-posedness;   

DOI  :  10.1016/j.cam.2012.02.013

来源: Elsevier

【 摘 要 】

We investigate the linear well-posedness for a class of three-phase boundary motion problems and perform some numerical simulations. In a typical model, three-phase boundaries evolve under certain evolution laws with specified normal velocities. The boundaries meet at a triple junction with appropriate conditions applied. A system of partial differential equations and algebraic equations (PDAE) is proposed to describe the problems. With reasonable assumptions, all problems are shown to be well-posed if all three boundaries evolve under the same evolution law. For problems involving two or more evolution laws, we show the well-posedness case by case for some examples. Numerical simulations are performed for some examples. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free