The fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the
visualization of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of …

In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with
degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour …

We analyse a novel mathematical model of malignant invasion which takes the form of a two-
phase moving boundary problem describing the invasion of a population of malignant cells …

Single-species reaction–diffusion equations, such as the Fisher–KPP and Porous-Fisher
equations, support travelling wave solutions that are often interpreted as simple …

In this paper, we study the orbital stability of traveling wave solutions to the Gallay and
Mascia (GM) reduction of the Gatenby–Gawlinski model. The heteroclinic solutions provided …

Motivated by tumor growth in Cancer Biology, we provide a complete analysis of existence
and non-existence of invasive fronts for the reduced Gatenby–Gawlinski model∂ t U= U f …

In this manuscript, we prove the existence of slow and fast traveling wave solutions in the
original Gatenby–Gawlinski model. We prove the existence of a slow traveling wave solution …

The Gatenby-Gawlinski model for the description of cancer invasion is taken into account
with the aim of investigating its structural aspects. From a phenomenological point of view …

We consider a Gatenby--Gawlinski-type model of invasive tumors in the presence of an
Allee effect. We describe the construction of bistable one-dimensional traveling fronts using …

Tumor invasion follows a complex mechanism which involves cell migration and
proliferation. To study the processes in which primary and secondary metastases invade …