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Basic principles and practical applications of the Cahn–Hilliard equation
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 …
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
Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour
growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and …
growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and …
A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis
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 …
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
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 …
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
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 …
tumor growth which was proposed by Hawkins–Daruud et al in Hawkins–Daruud et al (2011 …
On a diffuse interface model of tumour growth
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 …
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 …
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
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 …
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
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 …
growth. The model describes the growth of a tumor surrounded by host tissues in the …