Phase-field modelling is still a young discipline in condensed-matter physics, which
established itself for the class of systems that can be characterised by domains of different …

A new diffuse interface model for a two-phase flow of two incompressible fluids with different
densities is introduced using methods from rational continuum mechanics. The model fulfills …

How to develop efficient numerical schemes while preserving energy stability at the discrete
level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper …

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

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 …

In this article, we investigate numerical schemes for solving a three component Cahn-
Hilliard model. The space discretization is performed by using a Galerkin formulation and …

This paper is concerned with the motion of a time‐dependent hypersurface∂ Ω (t) in ℝ d that
evolves with a normal velocity where κ is the mean curvature of∂ Ω (t), and g is an external …

Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are
derived from balance equations and an energy inequality so that thermodynamic …

A phase field approach for structural topology optimization which allows for topology
changes and multiple materials is analyzed. First order optimality conditions are rigorously …

A phase field model for tumour growth is introduced that is based on a Brinkman law for
convective velocity fields. The model couples a convective Cahn-Hilliard equation for the …