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}
}

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

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

  • T. Fukao
  • Mathematics
    System Modelling and Optimization
  • 2015
TLDR
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

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

TLDR
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

TLDR
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.

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

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

  • Luca Scarpa
  • Mathematics
    Applied 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

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

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

SHOWING 1-10 OF 24 REFERENCES

Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary

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

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

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

The Cahn–Hilliard equation with time-dependent constraint

Multi-dimensional stefan problems with dynamic boundary conditions

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

A Cahn-Hilliard-Gurtin model with dynamic boundary conditions

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

On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions

The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered and well-posedness results are proved.

The Cahn-Hilliard Equation with Logarithmic Potentials

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