(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen
This paper deals with an initial and boundary value problem for a
system coupling equation and boundary condition both of CahnHilliard type; an
additional convective term with a forced velocity field, which could act as a
control on the system, is also present in the equation. Either regular or
singular potentials are admitted in the bulk and on the boundary. Both the
viscous and pure CahnHilliard cases are investigated, and a number of results
is proven about existence of solutions, uniqueness, regularity, continuous
dependence, uniform boundedness of solutions, strict separation property. A
complete approximation of the problem, based on the regularization of maximal
monotone graphs and the use of a FaedoGalerkin scheme, is introduced and
rigorously discussed.
