Related papers: Cahn-Hilliard equation on the boundary with bulk c…
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a…
Problems for partial differential equations coupled with dynamic boundary conditions can be viewed as a type of transmission problem between the bulk and its boundary. For the heat equation and the Allen-Cahn equation, various forms of such…
The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint which may involve either the solution inside…
The Cahn-Hilliard and viscous Cahn-Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved. Key words: Cahn-Hilliard…
We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic…
The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…
The Cahn--Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. In recent times, various dynamic boundary conditions have been introduced to model interactions of the materials with…
We consider a class of Cahn-Hilliard equation that characterizes phase separation phenomena of binary mixtures in a bounded domain $\Omega \subset \mathbb{R}^d$ $(d\in \{2,3\})$ with non-permeable boundary. The equations in the bulk are…
The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…
The well-known Cahn-Hilliard equation entails mass conservation if a suitable boundary condition is prescribed. In the case when the equation is also coupled with a dynamic boundary condition, including the Laplace-Beltrami operator on the…
The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…
A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach.…
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…
This paper is concerned with well-posedness of the Cahn-Hilliard equation subject to a class of new dynamic boundary conditions. The system was recently derived in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167-247) via an energetic…
A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation,…
A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. Key words: Cahn-Hilliard…
We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain $\Omega$ of $R^N$ and complemented with homogeneous Dirichlet boundary conditions of solid type (i.e., imposed in the entire complement of…
This work addresses the problem of solving the Cahn-Hilliard equation numerically. For that we introduce an abstract formulation for Cahn-Hilliard type equations with dynamic boundary conditions, we conduct the spatial semidiscretization…
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…
We consider a general class of bulk-surface convective Cahn--Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn--Hilliard type allow for dynamic…