3 papers
math.AP2025
Nonlinear partial differential equations in neuroscience: from modelling to mathematical theory
José A Carrillo, Pierre Roux
Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we br…
math.AP2024
Sharp critical mass criteria for weak solutions to a degenerate cross-attraction system
José Antonio Carrillo, Ke Lin
The qualitative study of solutions to the coupled parabolic-elliptic chemotaxis system with nonlinear diffusion for two species will be considered in the whole Euclidean space $\ma…
math.AP2024
Classical solutions of a mean field system for pulse-coupled oscillators: long time asymptotics versus blowup
José Antonio Carrillo, Xu'an Dou, Pierre Roux +1
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated…