# Separation property and convergence to equilibrium for the equation and dynamic boundary condition of Cahn–Hilliard type with singular potential

@article{Fukao2021SeparationPA, title={Separation property and convergence to equilibrium for the equation and dynamic boundary condition of Cahn–Hilliard type with singular potential}, author={Takeshi Fukao and Hao-qing Wu}, journal={Asymptotic Analysis}, year={2021} }

We consider a class of Cahn–Hilliard equation that models phase separation process of binary mixtures involving nontrivial boundary interactions in a bounded domain with non-permeable wall. The system is characterized by certain dynamic type boundary conditions and the total mass, in the bulk and on the boundary, is conserved for all time. For the case with physically relevant singular (e.g., logarithmic) potential, global regularity of weak solutions is established. In particular, when the…

## 8 Citations

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.…

On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and boundary penalization

- MathematicsJournal of Differential Equations
- 2021

Long-time behavior of the Cahn–Hilliard equation with dynamic boundary condition

- Mathematics
- 2020

We study the long-time behavior, within the framework of infinite dimensional dynamical systems, of the Cahn–Hilliard equation endowed with a new class of dynamic boundary conditions. The system…

Phase-field dynamics with transfer of materials: The Cahn-Hillard equation with reaction rate dependent dynamic boundary conditions

- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2021

A new model which interpolates between these previous models is introduced, and analytical properties such as the existence of unique solutions and convergence to the previous models mentioned above are investigated in both the weak and the strong sense.

Long-time dynamics of the Cahn–Hilliard equation with kinetic rate dependent dynamic boundary conditions

- MathematicsNonlinear Analysis
- 2022

A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions

- Mathematics
- 2021

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…

Stability of the semi-implicit method for the Cahn-Hilliard equation with logarithmic potentials

- MathematicsArXiv
- 2021

Strict phase separation and energy stability of the semi-implicit scheme are proved under natural constraints on the time step of the Cahn-Hilliard equation.

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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…

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