A review on the Cahn-Hilliard equation: classical results and recent advances in dynamic boundary conditions

H Wu - arXiv preprint arXiv:2112.13812, 2021 - arxiv.org
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 …

A boundary control problem for the viscous Cahn–Hilliard equation with dynamic boundary conditions

P Colli, G Gilardi, J Sprekels - Applied Mathematics & Optimization, 2016 - Springer
A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary
Conditions | SpringerLink Skip to main content Advertisement SpringerLink Log in Menu Find …

Optimal boundary control of a viscous Cahn--Hilliard system with dynamic boundary condition and double obstacle potentials

P Colli, MH Farshbaf-Shaker, G Gilardi… - SIAM Journal on Control …, 2015 - SIAM
In this paper, we investigate optimal boundary control problems for Cahn--Hilliard variational
inequalities with a dynamic boundary condition involving double obstacle potentials and the …

[HTML][HTML] Cahn–Hilliard equation with dynamic boundary conditions and mass constraint on the boundary

P Colli, T Fukao - Journal of Mathematical Analysis and Applications, 2015 - Elsevier
Abstract 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 …

A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions

P Colli, G Gilardi, J Sprekels - Advances in Nonlinear Analysis, 2015 - degruyter.com
A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary
conditions Page 1 Adv. Nonlinear Anal. ; ( ): – Research Article Pierluigi Colli*, Gianni Gilardi …

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

P Colli, T Fukao - Nonlinear Analysis: Theory, Methods & Applications, 2015 - Elsevier
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 …

On a logarithmic wave equation with nonlinear dynamical boundary conditions: local existence and blow-up

N Irkıl, K Mahdi, E Pişkin, M Alnegga… - Journal of Inequalities …, 2023 - Springer
This paper deals with a hyperbolic-type equation with a logarithmic source term and
dynamic boundary condition. Given convenient initial data, we obtained the local existence …

[HTML][HTML] On the Cahn–Hilliard equation with dynamic boundary conditions and a dominating boundary potential

P Colli, G Gilardi, J Sprekels - Journal of Mathematical Analysis and …, 2014 - Elsevier
On the Cahn–Hilliard equation with dynamic boundary conditions and a dominating
boundary potential - ScienceDirect Skip to main contentSkip to article Elsevier logo …

Two-phase flows through porous media described by a Cahn–Hilliard–Brinkman model with dynamic boundary conditions

P Colli, P Knopf, G Schimperna, A Signori - Journal of Evolution Equations, 2024 - Springer
We investigate a new diffuse-interface model that describes creeping two-phase flows (ie,
flows exhibiting a low Reynolds number), especially flows that permeate a porous medium …

Null controllability for semilinear heat equation with dynamic boundary conditions.

A Khoutaibi, L Maniar… - Discrete & Continuous …, 2022 - search.ebscohost.com
This paper deals with the null controllability of the semilinear heat equation with dynamic
boundary conditions of surface diffusion type, with nonlinearities involving drift terms. First …