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

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.