A Cahn–Hilliard system with forward-backward dynamic boundary condition and non-smooth potentials

A system with equation and dynamic boundary condition of Cahn–Hilliard type is considered. This comes from a derivation performed in Liu–Wu (Arch. Ration. Mech. Anal., 233:167–247, 2019) via an energetic variational approach. Actually, the related problem can be seen as transmission for phase variable bulk corresponding on boundary. The asymptotic behavior coefficient surface diffusion acting goes to 0 investigated. By this analysis we obtain forward-backward at limit. We deal general class potentials having double-well structure, including non-smooth double-obstacle potential. illustrate that limit well-posed by also proving continuous dependence estimate. Moreover, case when two graphs, boundary, exhibit same growth, show solution more regular prove error estimate suitable order parameter.