Finite speed of propagation for the Cahn–Hilliard equation with degenerate mobility

2019 ◽  
pp. 1-34
Author(s):  
Bosheng Chen ◽  
Changchun Liu
Keyword(s):  
Finite Speed Of Propagation ◽  
Finite Speed ◽  
Hilliard Equation ◽  
Degenerate Mobility ◽  
Speed Of Propagation ◽  
Cahn Hilliard Equation

scholarly journals Sharp-Interface Limits of the Cahn--Hilliard Equation with Degenerate Mobility

2016 ◽  
Vol 76 (2) ◽  
pp. 433-456 ◽  
Author(s):  
Alpha Albert Lee ◽  
Andreas Münch ◽  
Endre Süli
Keyword(s):  
Sharp Interface ◽  
Hilliard Equation ◽  
Degenerate Mobility ◽  
Cahn Hilliard Equation

scholarly journals Relaxation of the Cahn–Hilliard equation with singular single-well potential and degenerate mobility

2020 ◽  
Vol 32 (1) ◽  
pp. 89-112
Author(s):  
BENOÎT PERTHAME ◽  
ALEXANDRE POULAIN
Keyword(s):  
Hilliard Equation ◽  
Degenerate Mobility ◽  
Long Time ◽  
Single Well ◽  
Cahn Hilliard Equation ◽  
Long Time Asymptotics ◽  
Living Tissues ◽  
Entropy Structure ◽  
Second Order Equations ◽  
Relaxed System

The degenerate Cahn–Hilliard equation is a standard model to describe living tissues. It takes into account cell populations undergoing short-range attraction and long-range repulsion effects. In this framework, we consider the usual Cahn–Hilliard equation with a singular single-well potential and degenerate mobility. These degeneracy and singularity induce numerous difficulties, in particular for its numerical simulation. To overcome these issues, we propose a relaxation system formed of two second-order equations which can be solved with standard packages. This system is endowed with an energy and an entropy structure compatible with the limiting equation. Here, we study the theoretical properties of this system: global existence and convergence of the relaxed system to the degenerate Cahn–Hilliard equation. We also study the long-time asymptotics which interest relies on the numerous possible steady states with given mass.

Sign in / Sign up

Export Citation Format

Share Document