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

2015/05/27 by T. Fukao, Fukao, Takeshi · 1 citation
Computer Science · Materials Science · Mathematics · #35D30 #35K25 #35K61 #47J35 #80A22 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1505.07181

openalex publication_date 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials

Cited by

• Asymptotic analysis of the Allen-Cahn equation with dynamic boundary conditions of Cahn-Hilliard type

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