Cahn–Hilliard equation on the boundary with bulk condition of Allen–Cahn type

Abstract: The well-posedness of a system of partial differential equations with dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk Ω and on the boundary Γ. The Poisson equation for the chemical potential and the Allen–Cahn equation for the order parameter in the bulk Ω are considered as auxiliary conditions for solving the Cahn–Hilliard equation on the boundary Γ. Recently, the well-posedness of this equation with a dynamic boundary condition, both of Cahn–Hilliard type, was discussed. Based on this result, the existence of the solution and its continuous dependence on the data are proved.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Cahn–Hilliard equation on the boundary with bulk condition of Allen–Cahn type ; volume:9 ; number:1 ; year:2018 ; pages:16-38 ; extent:23 ; Advances in nonlinear analysis ; 9, Heft 1 (2018), 16-38 (gesamt 23)

Contributors, Places and Time

• Creator: Colli, Pierluigi ; Fukao, Takeshi

Further information

• DOI: 10.1515/anona-2018-0055
• URN: urn:nbn:de:101:1-2405021602357.607248241280
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 11:03 AM CEST