# On the longtime behavior of a viscous Cahn–Hilliard system with convection and dynamic boundary conditions

@article{Colli2018OnTL, title={On the longtime behavior of a viscous Cahn–Hilliard system with convection and dynamic boundary conditions}, author={Pierluigi Colli and Gianni Gilardi and J{\"u}rgen Sprekels}, journal={Journal of Elliptic and Parabolic Equations}, year={2018}, volume={4}, pages={327-347} }

AbstractIn this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous
convective Cahn–Hilliard system, which consists of two nonlinearly coupled second-order partial differential equations for the unknown quantities, the chemical potential and an order parameter representing the scaled density of one of the phases. In contrast to other contributions…

## 7 Citations

### Asymptotic limits and optimal control for the Cahn–Hilliard system with convection and dynamic boundary conditions

- MathematicsNonlinear Analysis
- 2019

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

- MathematicsAsymptotic Analysis
- 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…

### 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.…

### 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…

### Longtime behavior for a generalized Cahn-Hilliard system with fractional operators.

- Mathematics
- 2019

In this contribution, we deal with the longtime behavior of the solutions to the fractional variant of the Cahn-Hilliard system, with possibly singular potentials, that we have recently investigated…

### An asymptotic analysis for a generalized Cahn–Hilliard system with fractional operators

- Mathematics
- 2020

In the recent paper “Well-posedness and regularity for a generalized fractional Cahn–Hilliard system” (Colli et al. in Atti Accad Naz Lincei Rend Lincei Mat Appl 30:437–478, 2019), the same authors…

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