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

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• 作者：Zhenguo Pan^a ; ^{panzhenguo@gmail.com} ; Brian Wetton^b ; ^{wetton@math.ubc.ca}
• 关键词：Grain boundary ; Curvature motion ; Surface diffusion ; Three-phase problem ; Well-posedness
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2012
• 期刊代码：72_03770427
• 类别：cp
• 出版时间：July, 2012
• 卷：236
• 期：13
• 页码：3160-3173
• 文件大小：621 K

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.