4 papers · 2 filters
Growth of cancer stem cell driven tumors: staged invasion, linear determinacy, and the tumor invasion paradox
Montie Avery
We study growth of solid tumors in a partial differential equation model introduced by Hillen et al for the interaction between tumor cells (TCs) and cancer stem cells (CSCs). We f…
Front propagation close to the onset of instability
Montie Avery
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion syst…
Stability of coherent pattern formation through invasion in the FitzHugh-Nagumo system
Montie Avery, Paul Carter, Björn de Rijk +1
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are cri…
Pushed and pulled fronts in a logistic Keller-Segel model with chemorepulsion
Montie Avery, Matt Holzer, Arnd Scheel
We analyze spatial spreading in a population model with logistic growth and chemorepulsion. In a parameter range of short-range chemo-diffusion, we use geometric singular perturbat…