Basic principles and practical applications of the Cahn–Hilliard equation

J Kim, S Lee, Y Choi, SM Lee… - … Problems in Engineering, 2016 - Wiley Online Library
The celebrated Cahn–Hilliard (CH) equation was proposed to model the process of phase
separation in binary alloys by Cahn and Hilliard. Since then the equation has been …

A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport

H Garcke, KF Lam, E Sitka, V Styles - Mathematical Models and …, 2016 - World Scientific
Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour
growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and …

A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis

H Garcke, KF Lam, R Nürnberg… - Mathematical Models and …, 2018 - World Scientific
We derive a Cahn–Hilliard–Darcy model to describe multiphase tumour growth taking
interactions with multiple chemical species into account as well as the simultaneous …

Well-posedness of a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport

H Garcke, KF Lam - European Journal of Applied Mathematics, 2017 - cambridge.org
We consider a diffuse interface model for tumour growth consisting of a Cahn–Hilliard
equation with source terms coupled to a reaction–diffusion equation. The coupled system of …

Optimal distributed control of a diffuse interface model of tumor growth

P Colli, G Gilardi, E Rocca, J Sprekels - Nonlinearity, 2017 - iopscience.iop.org
In this paper, a distributed optimal control problem is studied for a diffuse interface model of
tumor growth which was proposed by Hawkins–Daruud et al in Hawkins–Daruud et al (2011 …

On a diffuse interface model of tumour growth

S Frigeri, M Grasselli, E Rocca - European Journal of Applied …, 2015 - cambridge.org
We consider a diffuse interface model of tumour growth proposed by A. Hawkins-Daruud et
al.((2013) J. Math. Biol. 67 1457–1485). This model consists of the Cahn–Hilliard equation …

[HTML][HTML] Analysis of a Cahn–Hilliard–Brinkman model for tumour growth with chemotaxis

M Ebenbeck, H Garcke - Journal of Differential Equations, 2019 - Elsevier
Phase field models recently gained a lot of interest in the context of tumour growth models.
Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often …

On a Cahn-Hilliard type phase field system related to tumor growth

P Colli, G Gilardi, D Hilhorst - ar**, delay-free, and invariant-set-preserving integrators for the viscous Cahn–Hilliard–Oono equation
H Zhang, L Liu, X Qian, S Song - Journal of Computational Physics, 2024 - Elsevier
Stabilization techniques are frequently used to construct efficient and stable schemes for stiff
and nonlinear systems. However, the introduced errors may lead to severe delay effects …

[HTML][HTML] On the long time behavior of a tumor growth model

A Miranville, E Rocca, G Schimperna - Journal of Differential Equations, 2019 - Elsevier
We consider the problem of the long time dynamics for a diffuse interface model for tumor
growth. The model describes the growth of a tumor surrounded by host tissues in the …