Convergence of Cahn-Hilliard systems to the Stefan problem with dynamic boundary conditions

Takeshi Fukao

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arXiv · 1505.07181

Convergence of Cahn-Hilliard systems to the Stefan problem with dynamic boundary conditions

Takeshi Fukao

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Abstract

This paper examines the well-posedness of the Stefan problem with a dynamic boundary condition. To show the existence of the weak solution, the original problem is approximated by a limit of an equation and dynamic boundary condition of Cahn-Hilliard type. By using this Cahn-Hilliard approach, it becomes clear that the state of the mushy region of the Stefan problem is characterized by an asymptotic limit of the fourth-order system, which has a double-well structure. This fact also raises the possibility of the numerical application of the Cahn-Hilliard system to the degenerate parabolic equation, of which the Stefan problem is one.

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Takeshi Fukao. 2015-05-27. Convergence of Cahn-Hilliard systems to the Stefan problem with dynamic boundary conditions. https://arxiv.org/abs/1505.07181

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