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We consider a general class of bulk-surface convective Cahn--Hilliard systemswith dynamic boundary conditions. In contrast to classical Neumann boundaryconditions, the dynamic boundary conditions of Cahn--Hilliard type allow fordynamic changes of the contact angle between the diffuse interface and theboundary, a convection-induced motion of the contact line as well as absorptionof material by the boundary. The coupling conditions for bulk and surfacequantities involve parameters $K,L\in[0,\infty]$, whose choice declares whetherthese conditions are of Dirichlet, Robin or Neumann type. We first prove theexistence of a weak solution to our model in the case $K,L\in (0,\infty)$ bymeans of a Faedo--Galerkin approach. For all other cases, the existence of aweak solution is then shown by means of the asymptotic limits, where $K$ and$L$ are sent to zero or to infinity, respectively. Eventually, we establishhigher regularity for the phase-fields, and we prove the uniqueness of weaksolutions given that the mobility functions are constant.

Well-posedness of a bulk-surface convective Cahn--Hilliard system with dynamic boundary conditions