3 papers
q-bio.PE2025
A phylogeny of biological patterns formed by nonlocal advection
Valeria Giunta, Thomas Hillen, Mark A. Lewis +1
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential…
q-bio.PE2025
Aggregation-diffusion in heterogeneous environments
Jonathan R. Potts
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to thei…
math.AP2024
Positivity and global existence for nonlocal advection-diffusion models of interacting populations
Valeria Giunta, Thomas Hillen, Mark Lewis +1
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the…