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 …

This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

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 …

In this article, we consider the Cahn–Hilliard–Brinkman–Ohta–Kawasaki tumor growth
system, which couples the Brinkman flow equations in the porous medium and the Cahn …

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 …

We consider a model describing the evolution of a tumor inside a host tissue in terms of the
parameters $\varphi_p $, $\varphi_d $(proliferating and dead cells, respectively), $ u $(cell …

In this work, we present a coupled 3D–1D model of solid tumor growth within a dynamically
changing vascular network to facilitate realistic simulations of angiogenesis. Additionally, the …

We propose a new type of diffuse interface model describing the evolution of a tumor mass
under the effects of a chemical substance (eg, a nutrient or a drug). The process is described …

We investigate the long-time dynamics and optimal control problem of a thermodynamically
consistent diffuse interface model that describes the growth of a tumor in presence of a …

Mechanical effects have mostly been neglected so far in phase field tumour models that are
based on a Cahn–Hilliard approach. In this paper we study a macroscopic mechanical …