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

2015/02/18 by Pierluigi Colli, Colli, Pierluigi, T. Fukao +1 · 2 citations
Computer Science · Materials Science · Mathematics · #35D30 #35D35 #35K25 #35K61 #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.1502.05159

openalex publication_date 2015/02/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a suitable setting for the conservation of a total mass in the bulk plus the boundary. A very general class of double-well like potentials is allowed. Moreover, some further regularity is obtained to guarantee the strong solution.

Citations

• Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary

Cited by

• Asymptotic analysis of transmission problems with parameter-dependent Robin conditions
• Long-time behavior of a nonlocal Cahn-Hilliard equation with nonlocal dynamic boundary condition and singular potentials
• Asymptotic analysis of the Allen-Cahn equation with dynamic boundary conditions of Cahn-Hilliard type

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