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

Authors:
Zhenguo Pan;Brian Wetton
Affiliations:
Department of Mathematics, National University of Singapore, Singapore 119076, Singapore;Department of Mathematics, University of British Columbia, Vancouver, B.C. Canada V6T 1Z2
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

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.