This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

In this survey article, a variety of systems modeling tumor growth are discussed. In
accordance with the hallmarks of cancer, the described models incorporate the primary …

Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour
growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and …

The Cahn–Hilliard equation and some of its variants Home 8.{{subColumn.name}} AIMS
Mathematics Search Advanced Home {{newsColumn.name}} 1.{{subColumn.name}} {{newsColumn.name}} …

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 …

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 …

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 …

The paper deals with a phase field system of Cahn-Hilliard type. For positive viscosity
coefficients, the authors prove an existence and uniqueness result and study the long time …

We consider an optimal control problem for a diffuse interface model of tumor growth. The
state equations couples a Cahn–Hilliard equation and a reaction-diffusion equation, which …

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 …