Journal
ANNALI DI MATEMATICA PURA ED APPLICATA
Volume 197, Issue 5, Pages 1445-1475Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10231-018-0732-1
Keywords
Cahn-Hilliard system; Convection; Dynamic boundary condition; Initial-boundary value problem; Well-posedness; Regularity of solutions
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Funding
- MIUR-PRIN Grant [2015PA5MP7]
- GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica)
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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 are 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.
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