On a Cahn--Hilliard system with convection and dynamic boundary conditions
- Colli, Pierluigi
- Gilardi, Gianni
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 35K61 35K25 76R05 80A22
- Cahn-Hilliard system, convection, dynamic boundary condition, in-tial-boundary value problem, well-posedness, regularity of solutions
This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of Cahn--Hilliard 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 Cahn--Hilliard 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 Faedo--Galerkin scheme, is introduced and rigorously discussed.
- Ann. Mat. Pura Appl. IV. Ser., 197 (2018), pp. 1445--1475, DOI 10.1007/s10231-018-0732-1 .