On a Cahn-Hilliard system with convection and dynamic boundary conditions
Pierluigi Colli, Gianni Gilardi, J\"urgen Sprekels
TL;DR
This paper studies a complex Cahn-Hilliard system with convection and dynamic boundary conditions, proving key properties like existence, uniqueness, and regularity of solutions, and introducing a rigorous approximation scheme.
Contribution
It introduces a comprehensive analysis of a Cahn-Hilliard system with convection and dynamic boundary conditions, including existence, uniqueness, regularity, and an approximation method.
Findings
Proved existence and uniqueness of solutions.
Established regularity and boundedness properties.
Developed a rigorous approximation scheme.
Abstract
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.
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On a Cahn–Hilliard system with convection
and dynamic boundary conditions
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centerPierluigi Colli*(1)*
e-mail: [email protected]
Gianni Gilardi*(1)*
e-mail: [email protected]
Jürgen Sprekels*(2)*
e-mail: [email protected]
(1) Dipartimento di Matematica “F. Casorati”, Università di Pavia
and Research Associate at the IMATI – C.N.R. Pavia
via Ferrata 5, 27100 Pavia, Italy
(2) Department of Mathematics
Humboldt-Universität zu Berlin
Unter den Linden 6, 10099 Berlin, Germany
and
Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstrasse 39, 10117 Berlin, Germany