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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…
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…
Global well-posedness and nonlinear stability of a chemotaxis system modeling multiple sclerosis
Laurent Desvillettes, Valeria Giunta, Jeff Morgan +1
We consider a system of reaction-diffusion equations including chemotaxis terms and coming out of the modeling of multiple sclerosis. The global existence of strong solutions to th…