42 citations · 47 across the 8 of their papers we have counts for
6 papers · 1 filter
Weakly nonlinear analysis of a two-species non-local advection-diffusion system
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection…
Detecting minimum energy states and multi-stability in nonlocal advection-diffusion models for interacting species
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent pa…
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…
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…
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,…
Mathematical Analysis of a Kinetic Model for Cell Movement in Network Tissues
Thomas Hillen, Peter Hinow, Zhi-An Wang
Mesenchymal motion describes the movement of cells in biological tissues formed by fiber networks. An important example is the migration of tumor cells through collagen networks du…