# Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials

@article{Colli2015EquationAD, title={Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials}, author={Pierluigi Colli and Takeshi Fukao}, journal={arXiv: Analysis of PDEs}, year={2015} }

## 49 Citations

### On a Cahn–Hilliard system with convection and dynamic boundary conditions

- Mathematics
- 2017

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…

### Cahn-Hilliard Approach to Some Degenerate Parabolic Equations with Dynamic Boundary Conditions

- MathematicsSystem Modelling and Optimization
- 2015

The main topic of this paper is the existence problem under an assumption for this maximal monotone graph for treating a wider class and the existence of a weak solution is proved.

### Cahn–Hilliard equation on the boundary with bulk condition of Allen–Cahn type

- MathematicsAdvances in Nonlinear Analysis
- 2018

Abstract The well-posedness of a system of partial differential equations with dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk…

### Convergence of Cahn-Hilliard systems to the Stefan problem with dynamic boundary conditions

- MathematicsAsymptot. Anal.
- 2016

It is clear that the state of the mushy region of the Stefan problem is characterized by an asymptotic limit of the fourth-order system, which has a double-well structure, which raises the possibility of the numerical application of the Cahn-Hilliard system to the degenerate parabolic equation.

### Nonlocal-to-Local Convergence of Cahn–Hilliard Equations: Neumann Boundary Conditions and Viscosity Terms

- MathematicsArchive for rational mechanics and analysis
- 2021

It is proved well-posedness for the nonlocal equation in a suitable variational sense and it is shown that the solutions to the non local equation converge to the corresponding Solutions to the local equation, as the convolution kernels approximate a Dirac delta.

### Existence and uniqueness of solutions to singular Cahn–Hilliard equations with nonlinear viscosity terms and dynamic boundary conditions

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

### A Boundary Control Problem for the Equation and Dynamic Boundary Condition of Cahn–Hilliard Type

- Mathematics
- 2017

A dynamic boundary condition is a type of partial differential equation that describes the dynamics of a system on the boundary. Combining with the heat equation in a smooth-bounded domain, the…

### The Stochastic Viscous Cahn–Hilliard Equation: Well-Posedness, Regularity and Vanishing Viscosity Limit

- MathematicsApplied Mathematics & Optimization
- 2020

Well-posedness is proved for the stochastic viscous Cahn–Hilliard equation with homogeneous Neumann boundary conditions and Wiener multiplicative noise. The double-well potential is allowed to have…

### The Cahn-Hilliard Equation with Forward-Backward Dynamic Boundary Condition via Vanishing Viscosity

- MathematicsSIAM J. Math. Anal.
- 2022

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…

### On a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentials

- MathematicsMathematische Nachrichten
- 2020

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.…

## References

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### The Allen–Cahn equation with dynamic boundary conditions and mass constraints

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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,…

### A Variational Approach to a Cahn–Hilliard Model in a Domain with Nonpermeable Walls

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We deal with the well-posedness and the long time behavior of a Cahn–Hilliard model with a singular bulk potential and suitable dynamic boundary conditions. We assume that the system is confined in a…

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We consider multi-phase Stefan problems for a class of nonlinear parabolic equations with dynamic boundary conditions formulated in bounded domains in RN, N≥2. Our dynamic boundary condition is…

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Our aim in this paper is to define proper dynamic boundary conditions for a generalization
of the Cahn-Hilliard system proposed by M. Gurtin. Such boundary conditions take into account
the…

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The Cahn-Hilliard equation with irregular potentials
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### The Cahn-Hilliard Equation with Logarithmic Potentials

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Our aim in this article is to discuss recent issues related with the Cahn-Hilliard equation in phase separation with the thermodynamically relevant logarithmic potentials; in particular, we are…