Equation and dynamic boundary condition of Cahn–Hilliard type with singular potentials. (November 2015)

• Record Type: Journal Article
• Authors: Colli, Pierluigi; Fukao, Takeshi
• Is Part Of: Nonlinear analysis. Volume 127(2015)
• Page Start: 413
• Page End: 433
• Publication Date: 2015-11
• Subjects: 35K61 -- 35K25 -- 35D30 -- 35D35 -- 80A22; Cahn–Hilliard system -- Dynamic boundary condition -- Mass conservation -- Well-posedness -- Strong solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.07.011
• Languages: English
• ISSNs: 0362-546X

Abstract

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.