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math.AP2021
Local and Global Existence for Non-local Multi-Species Advection-Diffusion Models
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has be…
math.AP2020★ 1 cited
Non-Local Cell Adhesion Models: Steady States and Bifurcations
Andreas Buttenschön, Thomas Hillen
In this manuscript, we consider the modelling of cellular adhesions, which is a key interaction between biological cells. Continuum models of the diffusion-advection-reaction type…
math.AP2019
Nonlocal Adhesion Models for Microorganisms on Bounded Domains
Thomas Hillen, Andreas Buttenschön
In 2006 Armstrong, Painter and Sherratt formulated a non-local differential equation model for cell-cell adhesion. For the one dimensional case we derive various types of adhesive,…